1 Definitions

2 Motivation

3 Approximating partial derivatives

4 An explicit numerical method for the heat equation

  4.1 Implementation

5 Stability of the simple explicit scheme

  5.1 Why is the stability constraint a problem?

6 The Crank-Nicolson method

  6.1 In general

  6.2 Stability of the Crank-Nicolson scheme

7 Cost -v- benefit