A new method of constructing two-level four-point explicit difference schemes with higher stability properties

Abstract

A class of new method of constructing two-level four-point explicit difference schemes with higher stability properties for a dispersive equation U _t = aU_xxx are proposed in this paper. Their local truncation errors are 0(τ + h) and stability conditions are |R|≤f(β), where/ is an increasing function of its variable. For examplef(0.1) = 0.262708,f(2) = 0.575258f(10) = 2.50013 andf(100) = 20 etc. These results are much better than |R|≤0.25 in [I] and seem to be the best for schemes of the same type at present.

Keywords:

• Two-level four-point explicit difference scheme
• dispersive equation
• higher stability

C.R. Categories:

• G.1.8