Learn · Numerical methods of Ordinary and Partial Differential Equations

Lecture 13 of 40

Stability Analysis of Multi Step Methods

Dr. G.P. Raja Sekhar · IIT Kharagpur

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Numerical methods of Ordinary and Partial Differential Equations, IIT Kharagpur (at NPTEL)
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CC BY-NC-SA, as NPTEL states it. Non-commercial use only.
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All the lectures

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