A comparison of finite difference schemes applied to the wave equation

Finite difference schemes have been given a great deal of consideration in recent years. Attention has been focused on the higher order schemes. Solutions of the linear system encountered in the study of finite difference schemes have been given considerable thought as well.

In this paper, we investigate schemes which belong to a higher order class of schemes known as the Collatz schemes. We investigate the idea of compactness as well as the linear systems produced by the schemes.