MATH 685/ CSI 700/ OR 682 Lecture Notes

Lecture 11.Ordinary differential equations.

Boundary value problems.

Boundary value problems

Boundary value problems

Example

Existence and uniqueness

Existence and uniqueness

Existence and uniqueness

Existence and uniqueness

Conditioning and stability

Numerical methods for BVPs

Shooting method

Shooting method

Example

Example

Example

Example

Example (cont.)

Multiple shooting

Finite difference method

Finite difference method

Finite difference method

Example

Example

Example (cont.)

Collocation method

Collocation method

Collocation method

Example

Example

Example (cont.)

Galerkin method

Galerkin method

Galerkin method

Galerkin method

Galerkin method

Galerkin method

Galerkin method example

Example

Example

Example (cont.)

Eigenvalue problems

Example

Example (cont.)