AISPDE2012: Finite Difference Method

Slides and computer programs used in the class are given below. First click on the links below which takes you to google drive. To download, go to File -> Download.

Slides

1. Introduction, some PDE models

2. Finite difference approximation

3. Finite difference for boundary value problem

4. Finite volume method for convection-diffusion problem

5. Finite difference for heat equation

6. Finite difference for linear scalar hyperbolic equation

Computer programs

1. 1-D BVP using central finite difference

   1. 2-D Poisson equation: Jacobi method, Gauss-Seidel Method, SOR Method

   2. 1-D steady convection, diffusion: central scheme, upwind scheme

   3. 1-D Heat equation: Forward Euler, Backward Euler, Crank-Nicholson

   4. 1-D linear, scalar convection equation: smooth solution with periodic BC, discontinuous solution

References

• 1. Thomee and Larsson, Partial Differential Equations with Numerical Methods, Springer

  2. R. J. LeVeque, Finite Difference methods for ordinary and partial differential equations, SIAM

  3. P. Wesseling, Principles of Computational Fluid Dynamics, Springer

  4. E. Suli, Numerical solution of PDEs, lecture notes, search on his website or get it here