Introduction
In HELM booklet 32.4 and 32.5, we saw methods of obtaining numerical solutions to Parabolic and Hyperbolic partial differential equations (PDEs). Another class of PDEs are the Elliptic type, and these usually model time-independent situations. In this Section we will concentrate on two particularly important Elliptic type PDEs: Laplace’s equation and Poisson’s equation.
Prerequisites
- familiarise yourself with difference methods for approximating second derivatives ( HELM booklet 31.3 )
- revise the Jacobi and Gauss-Seidel methods from ( HELM booklet 30.5)
Learning Outcomes
- obtain simple approximate solutions of certain elliptic equations
Contents
1 Elliptic equations2 A five point stencil
3 Systems of equations
4 Iterative methods
4.1 Jacobi iteration
4.2 Gauss-Seidel iteration
4.3 Convergence