一类恒稳定的三层差分格式

A Class of Three-level Difference Schemes With Absolute Stabilit

本文应用一种带参数的插值公式,构造了扩散方程和色散方程的相应差分格式,分析了它们的截断误差和稳定性条件,当适当取参数时,二者都是恒稳定的,且后者为高精度格式。

In this paper, a class of three-level difference schemes for the diffusion equatior u_t=au_(xx)(a>0) and the dispersion equative u_t=au_(xxx)(a>0 or a<0) are established respectively. These schemes are unconditionally stable when β> 1/2 for the former and β>1/3 for the latter. They are taken as a generalization of the Dufort-Frankel Scheme.