Numerical methods of Ordinary and Partial Differential Equations Video Lectures

Numerical methods of Ordinary and Partial Differential Equations
'Numerical methods of Ordinary and Partial Differential Equations' Video Lectures by Dr. G.P. Raja Sekhar from IIT Kharagpur
"Numerical methods of Ordinary and Partial Differential Equations" - Video Lectures
1. Motivation with few Examples
2. Single - Step Methods for IVPs
3. Analysis of Single Step Methods
4. Runge - Kutta Methods for IVPs
5. Higher Order Methods/Equations
6. Error - Stability - Convergence of Single Step Methods
7. Tutorial - I
8. Tutorial - II
9. Multi-Step Methods (Explicit)
10. Multi-Step Methods (Implicit)
11. Convergence and Stability of multi step methods
12. General methods for absolute stability
13. Stability Analysis of Multi Step Methods
14. Predictor - Corrector Methods
15. Some Comments on Multi - Step Methods
16. Finite Difference Methods - Linear BVPs
17. Linear/Non - Linear Second Order BVPs
18. BVPS - Derivative Boundary Conditions
19. Higher Order BVPs
20. Shooting Method BVPs
21. Tutorial - III
22. Introduction to First Order PDE
23. Introduction to Second Order PDE
24. Finite Difference Approximations to Parabolic PDEs
25. Implicit Methods for Parabolic PDEs
26. Consistency, Stability and Convergence
27. Other Numerical Methods for Parabolic PDEs
28. Tutorial - IV
29. Matrix Stability Analysis of Finite Difference Scheme
30. Fourier Series Stability Analysis of Finite Difference Scheme
31. Finite Difference Approximations to Elliptic PDEs- I
32. Finite Difference Approximations to Elliptic PDEs - II
33. Finite Difference Approximations to Elliptic PDEs - III
34. Finite Difference Approximations to Elliptic PDEs - IV
35. Finite Difference Approximations to Hyperbolic PDEs - I
36. Finite Difference Approximations to Hyperbolic PDEs - II
37. Method of characteristics for Hyperbolic PDEs - I
38. Method of characterisitcs of Hyperbolic PDEs - II
39. Finite Difference Approximations to 1st order Hyperbolic PDEs
40. Summary, Appendices, Remarks
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