Matrix Stability Analysis of Finite Difference Scheme 
Matrix Stability Analysis of Finite Difference Scheme
by IIT Kharagpur
◀ ← Video Lecture 29 of 40 → ▶
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Views: 1,872
Date Added: March 23, 2015

Lecture Description

This video lecture, part of the series Numerical Methods of Ordinary and Partial Differential Equations by Prof. , does not currently have a detailed description and video lecture title. If you have watched this lecture and know what it is about, particularly what Mathematics topics are discussed, please help us by commenting on this video with your suggested description and title. Many thanks from,

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Course Index

  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, and 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 Method
  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

Course Description

Course Outline: Ordinary Differential Equations: Initial Value Problems (IVP) and existence theorem. Truncation error, deriving finite difference equations. Single step methods for I order IVP- Taylor series method, Euler method, Picard’s method of successive approximation, Runge Kutta Methods. Stability of single step methods.
Multi step methods for I order IVP - Predictor-Corrector method, Euler PC method, Milne and Adams Moulton PC method. System of first order ODE, higher order IVPs. Stability of multi step methods, root condition. Linear Boundary Value Problems (BVP), finite difference methods, shooting methods, stability, error and convergence analysis. Non linear BVP, higher order BVP. (24 Lectures)

Partial Differential Equations: Classification of PDEs, Finite difference approximations to partial derivatives. Solution of one dimensional heat conduction equation by Explicit and Implicit schemes (Schmidt and Crank Nicolson methods ), stability and convergence criteria.
Laplace equation using standard five point formula and diagonal five point formula, Iterative methods for solving the linear systems. Hyperbolic equation, explicit / implicit schemes, method of characteristics. Solution of wave equation. Solution of I order Hyperbolic equation. Von Neumann stability. (16 Lectures)

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