In the preceding Section we looked at parabolic partial differential equations. Another class of PDE modelling initial value problems are of the hyperbolic type.
In this Section we will concentrate on the wave equation, which was introduced in HELM booklet 25.
- revise those aspects of HELM booklet 25 which deal with the wave equation
- familiarise yourself with difference methods for approximating first and second derivatives
- be familiar with the numerical methods used for parabolic equations
- obtain simple numerical solutions of the wave equation
2 Numerical solutions
3 The first time-step
3.1 Initial conditions
3.2 The first time-step