A Class of Three-Level Explicit Difference Schemes

Abstract

A class of three-level six-point explicit schemes $L_3$ with two parameters $s, p$ and accuracy $O(\tau h+h^2)$ for a dispersion equation $U_1=aU_{xxx}$ is established. The stability condition $|R|\leq 1.35756176$ $(s=3/2,p=1.184153684)$ for $L_3$ is better than $|R|$ ＜ 1.1851 in [1] and seems to be the best for schemes of the same type.