# 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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