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Analyzing Boundary Value Problems for Ordinary Differential Equations

This lecture note discusses the theory and applications of boundary value problems (BVPs) for ordinary differential equations. It covers fundamental concepts such as existence and uniqueness of solutions, conditioning, and stability of BVPs. Various numerical methods for solving BVPs are explored, including the shooting method, finite difference method, collocation method, and Galerkin method, along with practical examples for each approach. The notes also touch on eigenvalue problems, providing further insight into their significance and applications.

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Analyzing Boundary Value Problems for Ordinary Differential Equations

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  1. MATH 685/ CSI 700/ OR 682 Lecture Notes Lecture 11. Ordinary differential equations. Boundary value problems.

  2. Boundary value problems

  3. Boundary value problems

  4. Example

  5. Existence and uniqueness

  6. Existence and uniqueness

  7. Existence and uniqueness

  8. Existence and uniqueness

  9. Conditioning and stability

  10. Numerical methods for BVPs

  11. Shooting method

  12. Shooting method

  13. Example

  14. Example

  15. Example

  16. Example

  17. Example (cont.)

  18. Multiple shooting

  19. Finite difference method

  20. Finite difference method

  21. Finite difference method

  22. Example

  23. Example

  24. Example (cont.)

  25. Collocation method

  26. Collocation method

  27. Collocation method

  28. Example

  29. Example

  30. Example (cont.)

  31. Galerkin method

  32. Galerkin method

  33. Galerkin method

  34. Galerkin method

  35. Galerkin method

  36. Galerkin method

  37. Galerkin method example

  38. Example

  39. Example

  40. Example (cont.)

  41. Eigenvalue problems

  42. Example

  43. Example (cont.)

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