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Volume 8, Issue 3, March 2018
Journal of Basic and Applied Scientific
Research (JBASR)
An International Peer-reviewed journal
Number of issues per year: 12
ISSN: 2090-4304 (Print)
ISSN: 2090-424x (Online)
Copyright © 2018, TEXTROAD Publishing Corporation
J. Basic Appl. Sci. Res., Vol.8 No. 3: pp. 1-13, Year 2018
Journal of Basic and Applied Scientific Research (JBASR)
Monthly Publication
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Number of issues per year: 12 ISSN: 2090-4304 (Print)
ISSN: 2090-424x (Online) Journal of Basic and Applied Scientific Research (JBASR) is a peer reviewed, open access international scientific journal dedicated for rapid publication of high quality original research articles as well as review articles in the all areas of basic and applied sciences.
Journal of Basic and Applied Scientific Research (JBASR) is devoted to the rapid publication of original and significant research in...
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Table of Contents, March 2018
Adnan Nadeem, Turki Alghamdi, Ali Yawar, Amir Mehmood, Muhammad Shoaib Siddiqui
A Review and Classification of Flying Ad-Hoc Network (FANET) Routing Strategies
J. Basic Appl. Sci. Res. 2018 8(3): 1-8. [Abstract] [Full-Text PDF] [Full-Text XML]
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Umair Khalid Qureshi, Asif Ali Shaikh
Modified Cubic Convergence Iterative Method for Estimating a Single Root of Nonlinear Equations
J. Basic Appl. Sci. Res. 2018 8(3): 9-13. [Abstract] [Full-Text PDF] [Full-Text XML]
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J. Basic. Appl. Sci. Res., 8(3)1-8, 2018
© 2018, TextRoad Publication
ISSN 2090-4304
Journal of Basic and Applied
Scientific Research www.textroad.com
Corresponding Author: Adnan Nadeem, Faculty of Computer and Information System, Islamic University in Madinah, KSA. & Department
of Computer Science, Federal Urdu University of Arts, Science and Technology, Pakistan. E-mail: [email protected]
Received: January 2, 2018
Accepted: March 1, 2018
ABSTRACT
MANETs (Mobile Ad-hoc Networks) applications in various walks of life in the last two decades have resulted in introduction of its sub technologies such as VANETs (Vehicular Ad-hoc Network). In this paper, we focus on new ad hoc networking technology called FANET (Flying Ad-hoc Network). FANET introduces the ad hoc networking of flying UAVs to allow real
time communication between them and control stations. Flying drones can also form FANET to establish real time communication to achieve their mission. FANET will help in handling of the circumstances like crisis, natural disaster, military
combat zones, and package delivery. Efficient real-time routing is a major challenge in FANET because of the very high
mobility which results in unpredictable dynamic topology. Routing along with medium access control is a major hurdle in their
real time implementation. In this paper, we have first have first highlighted major research issues and challenges in FANET. Then we have performed an investigative review of suitability of using existing ad hoc routing protocols for FANETs. Then, we
propose five categories of FANET routing protocols: static, reactive, proactive, hybrid and hierarchical. Finally, we present a
comparison of routing strategies based on certain criteria’s. KEYWORDS— MANET, VANET, FANET, Routing protocols, UAVS, Sensor nodes
I. INTRODUCTION
A mobile ad-hoc network (MANET) is a mobile network of autonomous wireless devices with no backbone or
infrastructure but exhibits self-configuring characteristics. MANETs have many application areas such as, disaster relief, military
communication, urgent business meetings, etc. The main advantage of MANETs is their portability or mobility. The wide spread applications of MANETs has enabled sub categories of ad-hoc networking technologies, such as Vehicular Ad hoc Networks
(VANETs) and Flying Ad hoc Networks (FANETs). Usually, these networks have high mobility with rapid topology changes as
compared to a typical MANETs, because in both VANET and FANET, most of the nodes are vehicles and UAVs (Unmanned
Ariel Vehicles), respectively. VANETs are the networks in which vehicle to vehicle (V2V) and vehicle to pre-installed infrastructure communication is supported. The main objectives of VANETs are to improve, traffic efficiency and traffic
congestion, access to information and news to avoid accidents, and for entertainment purpose while driving. Flying Ad-hoc
Network (FANET) is a special type of MANET with support of very high mobility. In FANETs, the nodes are normally
Unmanned Aerial Vehicles (UAVs) in Unmanned Ariel Systems (UASs) environment. These networks are aimed to construct self-organizing networks with flying aircrafts in the sky [1]. UAVs are involved in both military and civilian applications. The
examples of applications of UAVs are, agricultural aviation governing [28], surveillance, patrolling the border area, traffic
management, pipe-line monitoring, seismic events, volcano monitoring [4], environmental monitoring, etc. Single UAVs frameworks have been utilized for quite a long time. Although single UAV systems are very often in use, but adding multiple
UAVs is a very fruitful idea due to its advantages over single UAV system. Therefore, these types of systems called multi-UAVs
system. In single UAV architectures, the UAVs are connected to either base station located in the ground or connected with a
satellite station for communication in star topology manners. In contrast to single UAV system, multi-UAVs systems have more than one UAV, therefore, multi-UAV can work in multi-hop scenario, and there is no need of all the UAVs to connect directly to
the earth station or satellite station.
Besides this, certain advantages and challenges are associated with Multi-UAVs systems. Some of the advantages over single UAV system are given below:
Economical: The maintenance and installation cost of large UAVs, is much higher than that of a small UAV (used in single
UAV system) [1].
Scalability: The coverage area of single UAV system is small as compared to multi-UAVs, hence, coverage rate is low [2] while, multi-UAVs systems have the ability to adapt to a situation easily.
Stability: One of the major drawbacks of single UAV system is the single point of failure i.e. if a UAV fails to complete its
task then the task will not be completed until another UAV is sent. While in multi-UAVs if one UAV fails then the task can be
A Review and Classification of Flying Ad-Hoc Network (FANET)
Routing Strategies
Adnan Nadeem1, 2, Turki Alghamdi1, Ali Yawar2, Amir Mehmood2, Muhammad Shoaib Siddiqui1
1Faculty of Computer and Information System, Islamic University in Madinah, KSA 2Department of Computer Science, Federal Urdu University of Arts, Science and Technology, Pakistan
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Nadeem et al., 2018
done other UAVs through different routes.
Timewise efficient: It is obvious that as compare to one UAV, multiple UAVs work faster to complete a task [3].
Sustainability: Multi UAV systems are more sustainable than single UAV systems. Some challenges are also associated with Multi UAV systems which are given below:
Cost of the equipment: The cost of the complex hardware used for communication with either the ground station or satellite station is very expensive.
Reliability: The reliability of the communication is a big concern in multi-UAV system due to their high mobility. Very high mobility in multi-UAV system causes the communication links to make-and-break rapidly. Therefore, it will affect the reliability
of the data.
Coverage Area: Coverage area is the transmission range of a UAV (in meter unit) in which it can remain connected with the
ground station. To cope all these challenges, the introduction of ad-hoc network is the alternate solution. This ad-hoc network is called
FANET. FANET has the capability to solve this problem of communication between UAVs.
Figure 1. MANET, VANET and FANET [1]
Multi UAV systems may use star topology to connect to the base station. Some of the nodes (UAVs) correspond with base
station, which is situated somewhere at ground, and other nodes can correspond with space station which may be a satellite.
UAV-to-UAV communication using the infrastructure has some inherited design problem. UAVs must be outfitted with costly and entangled equipment to correspond with ground and satellite stations. Reliability of the communication in this highly
dynamic environmental is a real challenge.
The rest of the paper is organized as follows. Section II, presents the major research issues and challenges of FANET. We presents our review and classification of FANET routing protocol in Section III. In section IV, we present a comparative study. Finally, in section V we presents our conclusion and highlight future work.
II. RESEARCH ISSUES AND CAHALLENGES
Considering few similarities between FANET, MANET and VANET; FANET inherits some of the issues and challenges from
MANET and VANET. However, due to additional characteristics, such as, very high speed of UAVs in FANET, the routing
protocols require major review and investigation. So, the data routing between UAVs undergoes a serious challenge. The routing communications protocol must be able to update routing table or cache dynamically according to modification in the topology.
Previous protocol does not provide a reliable communication. So, there is a need of new communication protocol to provide a
flexible and reliable communication. There are also various issues related to transmission like, security overheads, loss of data packets, and use of energy. To some
extent, a FANET is not quite the same as customary MANETs and VANETs; but the main idea is the same: having dynamic nodes in an ad hoc manner. Consequently, in a FANET, a few difficulties are substantial as in a VANET while confronting with
extra difficulties. Many inquiries have been performed to build the productivity of system with flying nodes, there are as yet numerous unsolved issues, which ought to be investigated.
A. Routing:
In a FANET, routing of data between UAVs is a serious challenge, which is not same as the MANETs with low portability mobility conditions. As indicated by topology changes, routing tables must be updated dynamically. Most of existing routing
algorithms’ metric calculations are neglected in FANET to give a dependable correspondence between UAVs. Reliability of
routes is also a real challenge due to the very high mobility in FANET. Authors in [22] have suggested reliable routing protocol, however suitability of such routing techniques in FANET is required. Along these lines, there is a need of new research direction
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to calculate routing metrics and develop efficient routing algorithms and network models for developing an adaptable and
responsive ad hoc model.
B. Path Planning: In a large scale mission territory and multi-UAV operations, participation and coordination between UAVs are one of the most
important factors to increase the efficiency of a FANET. In such cases, each UAV needs to change its pathway, and new ones
ought to be re-computed progressively. Accordingly, new methods/algorithms are required to arrange the FANET nodes for organizing the clusters of UAVs.
C. Quality of Service (QoS):
A FANET can be utilized for transporting various types of goods to the customer residences such as the delivery drones from Amazons. They incorporate GPS maps, streaming video/voice, images, straightforward instant messages etc. Provision of
certain qualities to service [23] parameter such as delay, bandwidth and packet loss are essential for FANET applications.
Characterizing an exhaustive system for QoS-empowered middleware is a serious challenge that ought to be overcome because
of the exceedingly mobile and dynamic structure of FANET. Misbehaviors [24] of nodes in FANET could also affect the quality of services in their operations.
Coordination between UAVs and manned aircrafts: It is an inescapable fact that, later on with increased number of UAVs, the flights of UAVs must be coordinated with the manned aircraft. Similarly, in a military aspect, destruction of enemy aircraft may be achieved by utilizing a FANET or these UAVs can be utilized as electronic jammers. Furthermore, these UAVs can be used
as surveillance in foe zones.
III. CLASSIFICATION OF FANET ROUTING STRATEGIES
In this section, we first review some major research that leads to the concepts of FANET. Then, we present classification of
FANET routing protocols. Remote (wireless) correspondence ability, available for small and mid-sized, less expensive UAVs, are currently provided
commercially. Some of the UAVs are modified and are programmed, load with expensive equipment like cameras, storage,
sensors and processors. They show a high level of stability in air. Some are equipped with just essential control units [6]. The engineering of an ordinary UAV having systems like, control, monitoring, data processing and landing. The inner system
gives an extensive variety and capabilities, from routing to performing information exchange to ground stations. The UAV
market is yet developing, and UAVs are being utilized as part of new activities and in taking care of new issues each day.
Numerous organization are concerned with creating low cost UAV systems of related services [18].
Since FANETs nodes are mobile and ad hoc in nature, they imposes difficulties on the protocols used to help their wireless correspondence. In the UAVs communication system, the behavior and speed of UAVs are considered as advantageous. There
are additionally advantages when UAVs utilize wireless network system. Some are as under:
Because of line-of-sight propagation, UAVs provide on demand, excellent quality of unguided communication.
UAVs can be distinguishing, or detecting the information nodes everywhere throughout the wireless network system
which are powerfully and dynamically placed in the network system.
UAVs can refresh their routes to improve the better execution of wireless system structure.
UAVs have capability to carry and forward large amount of data.
A. FANET NETWORKING PROTOCOLS The main purpose of routing protocols is to find appropriate path for data transmission. There are wide range of protocols for
different applications in wireless networks, like pre-computed routing protocols, dynamic source routing protocols, on demand
routing protocols, flooding, cluster based routing protocols. FANET and VANET are the sub-set of MANET networks [2].
FANET protocols are divided into the following categories.
Static Protocols
Proactive Protocols
Reactive Protocols
Hybrid Protocols
Static Routing Protocols
A routing table of static routing protocol must be computed and loaded before the operation of UAV nodes and cannot be change until the operation ends. Every node communicates with other nodes (UAVs) or with station on the ground, and stores its
own information [10]. It is necessary to wait until mission ends in case of failure of updating the table that is why these protocols
are not fault tolerant.
Load Carry and Delivery Routing (LCDR): Load Carry and Delivery Routing (LCDR) is the first routing protocol in FANET. UAV carry data from a ground node, and it may be a video or image, fly and carry it through to the destination ground node
which can be a ground control station or military team.
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Data Centric Routing (DCR): Data Centric Routing (DCR) is a routing protocol in FANET in which the receiving node, either
a ground node or a UAV, scatters queries with a specific end goal to gather specific information from a particular zone. Data
aggregation algorithm may use for energy efficient data dissemination. This model involves minimum assistance, when small
numbers of UAVs are on the path. DCR allow three scopes in decoupling.
Space decoupling: communication nodes can be anywhere.
Time decoupling: Subscriber’s node transmitted data instantly or may be transmitted later.
Flow decoupling: Delivery can be accomplished constantly.
Figure 2. Routing Protocols in FANET
Figure 3. A FANET scenery of multi-UAV systems.
Proactive Routing Protocols
Proactive routing protocols manage all the tables of specific area and also gather routing information in a network. In FANET,
there are different driven protocols which are not similar to each other. Nodes updates routing tables according to the change in
topology. The routing protocol carries the latest information of nodes that is why there is no need to wait and select the path between sender and receiver. When the bandwidth is not used effectively (a lot of traffic between nodes) then this will not be
recommended for large communication networks. Other than that the protocol seems to be slow when topology is changed, or
failure occurs. Destination Sequenced Distance Vector (DSDV): In Destination Sequenced Distance Vector (DSDV) routing protocol, every
node behaves like a router. It is a proactive routing protocol with table driven approach, where every node can maintain its
routing table and contains sequence number for each node. There updating mechanism works when network topology changes. For dynamic networks this protocol is not suitable because of the rapid changes in topology and does not support multipath routing.
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Optimized Link State Routing Protocol (OLSR): In OLSR routing protocol use two types of messages for network that are
“hello” and “topology control message”. In the communication range “hello” message is use for finding the neighbor nodes to
generate neighbor node list for each node and broadcasted to one hop neighbor [9]. Whereas “topology control message” is used
in the network to maintain the topology information. Each node refreshes or recalculates its routing table because these messages periodically refresh the topology information. There is large amount of overheads in this protocols because of its periodic flooding nature. Multi point relay (MPR) is used for reducing these overheads [10].
Reactive Routing Protocols
In Reactive routing protocols, unless there is communication between the two nodes, there is no need to figure out a route
between them; that is the reason Reactive routing protocols are the also called on demand routing protocols. This mechanism
reduces the overhead problem of Proactive Routing Protocols. The utilization of bandwidth in (RRP) is good as there is no periodic messaging.
Dynamic Source Routing (DSR): It is a reactive protocol and designed for wireless mesh network. Sender determined the route
from source to destination node. Sender node sends request to its neighbor nodes, there may be several route request messages in
the network. Sender node send a unique request id to avoid the mixing of the sender node. Every node of the network must be related with route caches in which every one of the routes are available. The principle issue in this is to keep up and refresh the
route caches. Ad-hoc On-demand Distance Vector (AODV): AODV has the same on demand functions like DSR and the difference is
maintaining the routing table [4], [10]. Every node in DSR can store different entries in the table for every destination and
establish the path for data packet transfer from source to destination. Whereas in AODV it holds only one entry for each
destination and stores next hop information to each data communication. AODV routing protocol consists of three phases:
routing discovery, transmission of packet, and route maintenance. AODV routing messages type are route request, route reply, and route error.
Hybrid Routing Protocols: Hybrid Routing Protocols (HRP) are used to overcome the limitations of proactive and reactive routing protocols as reactive
protocols require more time to find routes and proactive protocols have control messages overhead. In Hybrid routing a network
is divided into different regions, proactive protocol is used for intra region routing whereas reactive protocol is used for inter region routing.
Zone Routing Protocol (ZRP): ZRP works on the concept of zones. Each node has an alternate zone and zones are separated
by predefined range called R. Where the neighboring nodes meet along the range lines. Proactive strategy is used for routing
inside the zone and is called intra zone [10]. Information sends right away, when source and destination nodes are in the same
zone. Reactive routing techniques are used when information is needed to be sent outside the zone. Temporarily Ordered Routing Algorithm (TORA): TORA is a scalable, efficient and adaptive algorithm. It finds various routes
among source and destination. Most likely, TORA is a complicated protocol and when any network system connect down the
control messages propagates the purpose of failure. TORA works well on larger networks but has higher overhead for smaller networks.
Hierarchical Routing Protocols
Hierarchical routing is the routing which is mainly based on cluster based topology. One of the major issue in hierarchical routing is the formation of the cluster. Two clustering formation algorithms are discussed here:
Mobility prediction clustering (MPA): A cluster formation algorithm is proposed for FANET in [19] namely called Mobility
prediction clustering. Due to high mobility scenario in FANET, the formation of clusters has rapidly updates, and this algorithm address this problem by predicting the updates regarding network topology. It forecast the structure of mobility of UAVs by
using structure prediction algorithm [20] and link expiration time mobility model. It selects the UAV with highest weighted sum
value of these models as cluster head (CH). The result showed that this CH selection scheme increases the clusters stability.
Clustering Algorithm: A clustering formation algorithm for UAV networking is proposed in [21]. In first, the cluster is constructed on ground for multi-UAV system and then updated during the flying operation. Then the clustering plan is calculated
for selection of the CHs according to the geographical information. Once the UAVs deployed, then cluster structure is adjusted
according to the mission information. Results showed that this algorithm can be used to increase the stability and guarantee the
ability of dynamic networking.
IV. COMPARATIVE STUDY
As specified before, there exist four essential routing protocols for FANET. In this segment, we fundamentally break down
and look at these essential FANET protocols. Table 1 introduces the relative study among these four FANET routing protocols
which are static, proactive, reactive, and hybrid protocols. We clarify each of the examination criteria with more subtle elements
in this area.
5
Nadeem et al., 2018
Table: 1 Comparisons among the Basic Routing Protocols in FANET Types of Protocols
Criteria Static Protocols Proactive Protocols Reactive Protocols Hybrid Protocols
Main Idea Static Table Table Driven Protocol On demand protocol Combination of Proactive
and Reactive protocols
Complexity Less Moderate Average Average
Route Route is Static Route is Dynamic Route is Dynamic Route is Dynamic
Topology Size Small Small Large Small and large
Memory Size extensive extensive Least memory space Medium memory space
Fault Tolerant Missing Missing Missing Mostly present
Bandwidth Utilization Best possible Least possible Best possible Moderate
Convergence Time Quicker Slower Mostly fast Medium
Signaling Overhead Missing Existing Existing Existing
Communication Latency Less Less High High
Mission Failure Rate High Low Low Very low
Popularity Least popularity Medium popularity Medium popularity Best popularity
Operation Fixed mission Dynamic mission Dynamic mission Dynamic mission
A. Main Idea
In Static protocol, the primary thought is that the routing information is unchangeable or fixed for a specific mission and is
stacked into the UAV before the mission. Whereas, Proactive protocol holds the present route data into the table. Reactive
protocol is on request/on demand protocol, at the point when the source requests destination route, it computes the route.
B. Complexity Complexity is comparatively low in static protocol, when destination is fixed. If there should be an occurrence of topology
change, route finding turns out to be more complicate in proactive convention.
C. Route If there should be an occurrence of static protocol, route is settled all through the mission. Routes are dynamic for every other
protocol.
D. Topology size Best utilization for fixed topology mission is Static protocol. Subsequently, if the size of the topology measures extensive,
then there is a possibility of change in topology. Thus, it is better to use Static protocol for small network systems. Proactive
protocol is a table-driven protocol. If the event that the quantity of UAVs expands, their comparing routing table sections
additionally increments. In this manner, proactive protocol is suitable for network with small number of nodes. For hybrid and intra zone routing mostly fixed and small network size is better.
E. Memory size Before the mission starts, the entire information about routing is transferred into the UAV in Static protocol. Accordingly, this
process requires large memory space. In the event that the number of nodes increases, the table size becomes bigger. In this manner, large memory space needed in Proactive protocol. Reactive protocols are mostly source driven protocol hence, when
source requires to discover a route, the route discovery mechanism would be actuated, hence, requiring less memory. Position-
based protocol stores the directions of each UAV, along these lines requiring large memory space.
F. Fault tolerant
Mission route or topology change in FANETs is a fundamental issue. Static protocol doesn’t support this situation. In this
way, fault tolerance is missing in this convention. Other routing mechanisms have some fault tolerance mechanism for finding
alternate routes.
G. Bandwidth utilization
Static protocols are utilized as a part of small network system where topology is fixed, so there is almost no use of bandwidth utilization. Hello messages are sent periodically by Proactive protocols in the system. Thus, this protocol requires more information exchange or require more bandwidth. Less transmission capacity is required for Reactive protocols because they are
source driven. For hybrid protocols, transmission capacity use is medium.
H. Convergence time
Destination is predefined in the static protocol. When a route is required, discovery time is minimum. After every change in the topology, proactive protocol looks through the destination node, resulting in bigger convergence time. Reactive protocol
discovers the route quick, however this protocol takes additional time when topology changes. Whereas Hybrid protocols need
average time to converge the network.
I. Signaling overhead
There are signaling overheads in Proactive, Reactive and Hybrid protocols; however, the Static protocols have no overhead. For
example, in proactive protocol overhead of hello messages, whereas, route request and route reply message in Reactive and
6
J. Basic. Appl. Sci. Res., 8(3)1-8, 2018
hybrid protocols.
J. Popularity
Static protocols are easy to understand; however, they are not blame tolerant. That is the reason, they are only used in static
small networks. Other protocols are easy to configure and can handle mobile and dynamic networks, therefore, they are significantly well known.
K. Communication latency
Since the path distance in between the UAVs is less and also have low correspondence in the static and proactive protocols, there is low communication latency. The distance between the UAV to UAV and ground station to UAV is higher in reactive and
hybrid protocols. Due to this Reactive and hybrid protocols holds much higher latency as compare to static and proactive
protocol. Also reactive protocols need time for route discovery, therefore, the communication latency increases.
L. Operation Static protocols are utilized as a part of missions where mission objective and topology are settled or fixed. Already, most of
the protocols were utilized as a part of military operations. However, utilization of UAVs has expanded day by day. Therefore,
numerous civilian operations are currently directed by multi- UAVs frameworks. Therefore, every protocol is being modified to
handle mobility and ad hoc nature, so these protocols can also utilize in civilian and military operations.
V. CONCLUSION UAVs have a promising part in a substantial operation zone with complex missions. UAVs require participation with each
other and need a fast and simple data communication framework. Multi UAV framework reduces the operation achievement time
and enhance the quality of the framework for airborne operations when contrasted with a single UAV framework. To apply
organizing in non-Line of Sight (LOS), urban, forceful, and loud condition, multi-UAV framework is extremely viable and precise. Correspondence is a critical issues for multi-UAV frameworks. In this research paper, specially appointed systems
among the UAVs, i.e. FANETs are studied alongside their main difficulties in contrast to the conventional ad hoc systems. The
current steering conventions for FANETs are grouped into five noteworthy classifications which are then basically broke down and analyzed in view of different execution criteria. At last, we have listed a few open research issues concerned with FANET,
which allow the research community to focus on.
REFERENCES
[1] Tareque, Md Hasan, Md Shohrab Hossain, and Mohammed Atiquzzaman. "On the routing in flying ad hoc networks."
In Computer Science and Information Systems (FedCSIS), 2015 Federated Conference on, pp. 1-9. IEEE, 2015.
[2] Kaur, Simarjot, and Meenu Talwar. "Routing Strategies in Flying Ad-Hoc Networks." Journal of Network Communications
and Emerging Technologies (JNCET) www. jncet. org 6, no. 3 (2016).
[3] Bujari, Armir, Carlos T. Calafate, Juan-Carlos Cano, Pietro Manzoni, Claudio Enrico Palazzi, and Daniele Ronzani. "Flying
ad-hoc network application scenarios and mobility models." International Journal of Distributed Sensor Networks13, no. 10
(2017): 1550147717738192.
[4] Maistrenko, Vasily A., Leonov V. Alexey, and Volkov A. Danil. "Experimental estimate of using the ant colony
optimization algorithm to solve the routing problem in FANET." In Control and Communications (SIBCON), 2016
International Siberian Conference on, pp. 1-10. IEEE, 2016.
[5] Bilal, Rabia, and Bilal Muhammad Khan. "Analysis of Mobility Models and Routing Schemes for Flying Ad-Hoc Networks
(FANETS)." International Journal of Applied Engineering Research 12, no. 12 (2017): 3263-3269.
[6] Farhan Mohammed, Imad Jawhar, Nader Mohamed, Idries, “Towards Trusted and Efficient UAV-Based Communication”,
2nd International Conference on Big Data Security on Cloud, IEEE International Conference on High Performance and
Smart Computing, IEEE International Conference on Intelligent Data and Security, 2016 IEEE
[7] Stefano Rosati, Karol Kru˙zelecki, Gr´egoire Heitz, Dario Floreano,Bixio Rimoldi, “Dynamic Routing for Flying Ad Hoc
Networks, Transactions on Vehicular Technology, 2015 IEEE
[8] Kuldeep Singh,Anil Kumar Verma, “Applying OLSR Routing in FANETs”, International Conference on Advanced
Communication Control and Computing Technologies, 2014 IEEE
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International Siberian Conference on Control and Communications, 2016.
[10] Krishan Yadav, Amit Nain, Sunil Maakar, Bahal Bhiwani, “Routing Protocols in FANET: Survey”, National Conference on
Innovative Trends in Computer Science Engineering, April 4, 2015
[11] Anuradha Chauhan, Ms. Renu Singla, “A Detail Review on Unmanned Aeronautical Ad-hoc Networks”, International
Journal of Science, Engineering and Technology Research (IJSETR) Volume 5, Issue 5, May 2016.
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[12] Sameer Qazi, Arsalan Alvi, Adil Mazhar Qureshi, Bilal A. Khawaja,Muhammad Mustaqim, “An Architecture for Real Time
Monitoring Aerial Adhoc Network”, 13th International Conference on Frontiers of Information Technology, 2015
[13] Alireza Talischi, “A Review: QoS and PDR at Flying Ad-Hoc Networks (FANETs) Routing Protocols”,
[14] Dr S.Vijayalakshmi, M.Sweatha, “A Survey on History and Types of Manet” International Journal of Emerging Trends in
Science and Technology, 2016.
[15] Ozgur Koray Sahingoz, “Networking Models in Flying Ad-Hoc Networks (FANETs): Concepts and Challenges”, Springer
Science+Business Media Dordrecht 2013.
[16] Muhammad Asghar Khan, Raees Muhammad Asif, Syyed Muhammad Riaz uddin, Alif Shah, “ Review of Communication
Protocols for FANETs (Flying Ad-Hoc Networks)”, International Conference on Engineering and Emerging echnologies
(ICEET-2015) March 26-27, 2015; Superior University Lahore Pakistan.
[17] Smriti Iyer, “Review of Flying Ad-hoc Networks (FANETs)”, International Journal on Recent and Innovation Trends in
Computing and Communication, Volume: 4 Issue: 3
[18] Volodymyr Kharchenko, Dmitry Prusov, “ANALYSIS OF UNMANNED AIRCRAFT SYSTEMS APPLICATION IN THE
CIVIL FIELD”, 2012 Volume 27(3): 335–343.
[19] Zang, Chunhua, and Shouhong Zang. "Mobility prediction clustering algorithm for UAV networking." In GLOBECOM
Workshops (GC Wkshps), 2011 IEEE, pp. 1158-1161. IEEE, 2011.
[20] Konstantopoulos, Charalampos, Damianos Gavalas, and Grammati Pantziou. "A mobility aware technique for clustering on
mobile ad-hoc networks." Lecture Notes in Computer Science 4308 (2006): 397.
[21] Liu, Kesheng, Jun Zhang, and Tao Zhang. "The clustering algorithm of UAV networking in near-space." In Antennas,
Propagation and EM Theory, 2008. ISAPE 2008. 8th International Symposium on, pp. 1550-1553. IEEE, 2008.
[22] NM Obaid Khan, Adnan Nadeem, Kamran Ahsan, “RPRP: Routing Protocol to ensure the reliability in health care system”,
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J. Basic. Appl. Sci. Res., 8(3)9-13, 2018
© 2018, TextRoad Publication
ISSN 2090-4304
Journal of Basic and Applied
Scientific Research www.textroad.com
Corresponding Author: Umair Khalid Qureshi, Department of Basic Science & Related Studies, Mehran University of Engineering and technology, Pakistan. Email:[email protected]
Modified Cubic Convergence Iterative Method for Estimating a Single Root
of Nonlinear Equations
Umair Khalid Qureshi*, Asif Ali Shaikh
Department of Basic Science & Related Studies, Mehran University of Engineering and technology, Pakistan
Received: December 23, 2017
Accepted: March 1, 2018
ABSTRACT
This study has been developed a Modified Iterative Method for estimating a single root of nonlinear equations and
analyzed. The proposed Modified Technique is a Modification of Regula-Falsi Method and Newton Raphson
Method, and it is cubic order of convergence. The Modified Cubic Convergence Method faster than cubic
Methods such as variant of Newton Raphson Method and Halley Method. The comparison in table-1 for different test functions demonstrate the faster convergence of proposed method. EXCEL and C++ are implemented for the
results and graphical representations.
KEYWORD: Non-linear equations, cubic methods, order of convergence, Absolute percentage error, accuracy
1. INTRODUCTION
Finding roots of nonlinear equations efficiently has widespread applications in numerous branches of pure
science and applied science, it is deliberated in general framework of the nonlinear equations [2], such as non-
linear equations
���� � 0
For estimating a root of non-linear equations���� � 0, utmost researchers and scientists took interest and lots of
variants of accelerated methods had been introduced. Such as most commonly used bracketing techniques includes bisection method and regula-falsi method [1]. These methods are useful bracketing techniques which require two
initial guesses. Both techniques are linear convergence order, while in some cases regula-falsi technique struggles due to sluggish convergence. Besides, Newton Raphson Method are fast converging numerical techniques but are not reliable because keeping a kind of pitfall [3].
�� � ��– ������`���� Where n=0,1,2, …
However, it is most valuable and modest numerical techniques. In recent years, in literature several modifications
had been done by using these techniques for solving nonlinear equations [4-6].Furthermore, modification in Newton Raphson Method to increasing order of convergence and computational efficacy a Variant of Newton Raphson
Technique had been proposed by using Quadrature rule [9], such as
� � ��– ������`���� �� � �� � 2������`���� � �`� ��
Similar investigation, combined the Bisection, Regula-Falsi and Newton Raphson techniques are given some techniques for solving non-linear equations with better accuracy sight as well as iteration perspective [7-8].
Correspondingly, in this paper a Modified cubic iterated method has been suggested. The proposed method is
assortment of regula-falsi method and Newton Raphson Method. The Modified cubic method has been compared
9
Qureshi and Shaikh, 2018
with cubic method in reference [9, 10]. The Modified Method is fast converging and more efficient to approaching
the root.
2. MODIFIEDITERATEDMETHOD
The new developed iterative method is based on Regula-Falsi Method and Newton Raphson Method, such as
�� � �� � � � ���� �� � ����� ����� Or�� ��1�
�� � ���� �� � �������� �� � �����
Where,
� � ��– ������`���� � � ��2� By using �2����1�, we get
�� � �� ���– �����
�`���� � ��� ���– �����
�`����� � ����� ����� or
�� � �� ��– �����
�`������ ���– �����
�`����� � ����� ����� Finally, we obtain
�� � �� � ������������`���� � �`����� ���– �����
�`�����
Hence this is a proposed method.
3. CONVERGENCE ANALYSIS
This segment has shown that the developed Method is keeping cubic convergence by using Taylor series expansion.
Proof:
Using the relation�� � �� � a in Taylor series, therefore from Taylor series we estimate
�����, �`������ � ���– ������`����� with using this condition c � �``�"���`�"� and ignoring higher order term for easy to
solve, such as
����� � �`������ � #���� � � ���� �`���� � �`����1 � 2#��� � � �����
By using ����� �������2�, we get
� � �� � �`������ � #�����`����1 � 2#��� � � ��$���1 � #����1 � 2#���$ � � ��$���1 � #����1 � 2#��� � � ��$���1 � #��� � � c���Thus, �� �� � �`����c��� � #%��&��� �� � c����`����1 � #����� '(� )��– ������`����* � c����`����1 � #����� � � ������
10
J. Basic. Appl. Sci. Res., 8(3)9-13, 2018
By using ���, ������ ��������3�, we get
�� � �� � �`������ � #�����`������ � #�����`������ � #�����`����1 � 2#��� � �`����1 � 2#���c����`����1 � #������� � �� � [���1 � #����1 � 2#���$]�1 � #��� � c���1 � #����� �1 � #����� � �� � [����1 � #����1 � 2#���]�1 � #����c�� � #%�%� � 1� #��� �� � �� � [����1 � #�� � 2#�����]�1 � #����#%�%� � 1�
�� � �� � [���1 � #�� � 2#���� � #�� � #���� � 2#%�%��]�1 � #%�%��$�� � �� � ���1 � 3#���� � 2#%�%���1 � #%�%���� � �� � ���1 � 3#���� �2#%�%� � #%�%� � 3#.�.� � 2#/�/���� � �� � �� � 3#��%� � #%�&� � 3#.�/� � 2#/�0���� � 3#��%� � #%�&� � 3#.�/� � 2#/�0�Hence this has been proven that the established iterative method is cubic order of convergence.
4. NUMERICAL RESULTS
This segment the established method is practical on few examples of nonlinear equations and tested developed method with the variant of Newton Raphson Method [11]
� � ��– ������`���� �� � �� � 2������`���� � �`� ��
and Halley Method [12]
�� � �� � 2������`����2�`����� � ������``����
From numerical result in table-1, it has been detected that the cubic iterative method is reducing the number of
iterations which is less than the number of iteration of cubic methods and likewise accuracy side. Mathematical package such as C++ and EXCEL have used to justify the proposed Iterative Method. From the results and
comparison of proposed cubic iterative method with the cubic methods that the proposed cubic iterative method is well execution than prevailing cubic methods.
Table-1 FUNCTIONS METHODS ITERATIONS X A E%
Sinx-x+1
X=2
Halley Method
Variant Newton Method
New Method
2
3
2
1.93456
4.33922e-5
1.19209e-7
3.01600e-5
2x-lnx-7
X=4
Halley Method
Variant Newton Method
New Method
3
2
2
4.21991
3.10421e-4
1.19209e-5
2.86102e-6
x3 -9x+1
X=0
Halley Method
Variant Newton Method
New Method
2
4
2
0.111264
1.53050e-4
1.49012e-7
4.24683e-7
Cosx-x3
X=1
Halley Method
Variant Newton Method
New Method
2
6
2
0.865474
1.28573e-3
1.78814e-7
1.76102e-3
xex–2
X=3
Halley Method
Variant Newton Method
New Method
5
10
5
0.852605
5.96046e-8
5.96046e-8
2.98023e-8
11
Qureshi and Shaikh, 2018
5. CONCLUSION
This paper a Modified Iterated Method has been designed to find the root of nonlinear equations. The
Modified Iterated Method has a cubic order of convergence, and it is derived from Regula-Falsi Method and Newton Raphson Method. Throughout the study, it can be concluded that the Modified Cubic Method is good execution and
fast converging technique to approaching the root for the assessment of variant of Newton Raphson Method and Halley Method. Henceforth the proposed method is superior and performing well for estimating a root of non-linear
equations.
REFERENCES
[1] Solanki C., P. Thapliyal and K. Tomar, Role of Bisection Method, International Journal of Computer
Applications. Technology and Research Volume 3– Issue 8, 535 - 535, 2014.
[2] Iwetan, C. N., I. A. Fuwape, M. S. Olajide, and R. A. Adenodi, (2012), Comparative Study of the Bisection and
Newton Methods in solving for Zero and Extremes of a Single-Variable Function. J. of NAMP Vol.21 173-176.
[3] Akram, S. and Q. U. Ann., 2015, Newton Raphson Method, International Journal of Scientific &Engineering
Research, Volume 6.
[4] Siyal, A. A. R. A. Memon, N. M. Katbar, and F. Ahmad, 2017, Modified Algorithm for Solving Nonlinear Equations in Single Variable, J. Appl. Environ. Biol. Sci., 7(5)166-171, 2017.
[5] Somroo, E., 2016. On the Development of New Multi-Step Derivative Free Method to Accelerate the
0
1
2
3
4
5
6
7
1 2 3
Figure-1: Comparative Illustration A E % of sinx-x+1
0
5
10
15
20
1 2 3
Figure-2: Comparative Illustration A E% of 2x-lnx-7
12
J. Basic. Appl. Sci. Res., 8(3)9-13, 2018
Convergence of Bracketing Methods for Solving, Sindh University Research Journal (Sci. Ser.) Vol. 48(3) 601-
604.
[6] Sangah, A. A., 2016. Comparative study of Existing bracketing methods with modified Bracketing algorithm for
Solving Non-Linear Equation in single variable, Sindh University. Research Journal (Sci.Ser.) Vol. 48 (1) 171-174 (2016).
[7] Siyal, A. A., 2016. Hybrid Closed Algorithm for Solving Nonlinear Equations in one Variable, Sindh University
Research Journal (Sci. Ser.) Vol. 48 (4) 779-782.
[8] Allame M., and N. Azad, 2012.On Modified Newton Method for Solving a Nonlinear Algebraic Equations by
Mid-Point, World Applied Sciences Journal 17 (12): 1546-1548, ISSN 1818-4952 IDOSI Publications.
[9] Weerakoon, S. And T. G. I. Fernando, A Variant of Newton’s Method with Accelerated Third-Order
Convergence, Applied Mathematics Letters 13, 87-93.
[10] E. Halley, A new exact and easy method for finding the roots of equations generally and without any previous reduction, Phil. Roy. Soc. London 8, 136-147
13
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procedures should be mentioned briefly. Capitalize trade names and include the manufacturer's name and address. Subheadings
should be used. Methods in general use need not be described in detail.
Results
Results should be presented in a logical sequence in the text, tables and figures; repetitive presentation of the same data in different
forms should be avoided. The results should not contain material appropriate to the Discussion. It should be written in the past tense
when describing findings in the authors' experiments. Results should be explained, but largely without referring to the literature.
Discussion
The discussion should consider the results in relation to any hypotheses advanced in the Introduction and place the study in the
context of other work. Results and Discussion sections can be combined.
Conclusions
If an optional conclusion section is used, its content should not substantially duplicate the abstract.
Acknowledgment
The acknowledgments of people, grants, funds, etc should be brief.
References
Bibliographic references in the text appear like [1, 2, 5, 6], using square brace in superscript. References should be numbered
consecutively, with style:
Journal paper:
1. Hadjibabaie, M., N. Rastkari, A.Rezaie and M. Abdollahi, 2005. The Adverse Drug Reaction in the Gastrointestinal Tract: An
Overview. Intl. J. Pharmacol., 1 (1): 1-8.
Books:
1. Daniel A. Potter, 2002. Destructive turfgrass insects: Biology, diagnosis and control. Wiley Canada Publishers, pp: 24-67.
Chapters in Book:
1. Bray R.A., 1994. The leucaena psyllid. In: Forage Tree Legumes in Tropical Agriculture (eds R.C. Gutteridge and H.M. Shelton) pp.
283–291. CAB International, Oxford.
Titles of journals should be given in full. ‘In press' can only be used to cite manuscripts actually accepted for publication in a journal.
Citations such as ‘manuscript in preparation' or ‘manuscript submitted' are not permitted. Data from such manuscripts can only be
mentioned in the text as ‘unpublished data'.
A Report:
1. Makarewicz, J.C., T. Lewis and P. Bertram, 1995. Epilimnetic phytoplankton and zooplankton biomass and species composition in
Lake Michigan, 1983-1992. U.S. EPA Great Lakes National Program, Chicago, IL. EPA 905-R-95-009.
Conference Proceedings:
1. Stock, A., 2004. Signal Transduction in Bacteria. In the Proceedings of the 2004 Markey Scholars Conference, pp: 80-89.
A Thesis:
1. Strunk, J.L., 1991. The extraction of mercury from sediment and the geochemical partitioning of mercury in sediments from Lake
Superior, M. S. thesis, Michigan State Univ., East Lansing, MI.
Tables and Equations
Tables and equations should not be submitted in a format exceeding the A4 page size (in portrait form). All tables should be
embedded within the manuscript, and must be captioned and numbered sequentially. Each table should be on a separate
page, numbered consecutively in Arabic numerals and supplied with a heading and a legend. Tables should be self-explanatory
without reference to the text.
Figures / Illustrations / Photographs
Graphics should be supplied as high resolution (at least 300-600 dp.i.) electronic files. Digital images supplied only as low-resolution
print-outs cannot be used. Graphs, diagrams, chromatograms, photos, etc. should be prepared as clear, original positives, suitable
for reproduction. All figures should be embedded within the manuscript, and must be captioned and numbered
sequentially.
Proofs
Proofs will be sent via e-mail as an Acrobat PDF file (e-mail attachment) and should be returned within 3 days of receipt. Page proofs
are considered to be the final version of the manuscript. With the exception of typographical or minor clerical errors, no changes will
be made in the manuscript at the proof stage.
Check List
We recommend that you ask a colleague to read over your paper prior to submission to ensure it is of a high standard and conforms
to a high level of scientific writing.
Before submission of your manuscript, please check that:
• All references cited in the text are included in the reference section.
• All figures and tables are cited in the text.
• Figures are at least 300 d.p.i.
• The pages are numbered.
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