色散方程的一类双步长指数型三层显格式

A kind of the Exponent Type of Twofold Step Three-Level Explicit Schemes For The Dispersive Equation

本文给出了求解色散方程 ut=au_(xxx)的一类双步长指数型三层显格式,其中间层包含七个节点。文章分析了该差分格式的截断误差,导出了该格式的稳定性条件为r|≤3e^(kh)(K≥0为参数,h 为空间步长)。当 K=0时,|r|≤3,它优于文[2]和[3]的结果|r|≤2.3945;当 K=4时、h=(π/64)时、|r|≤3.6508,是[2]、[3]的结果的1.5倍。

This paper constructs a kind of three-level explicit schemes of twofold step exp onent type,with seven knots in the middle level,for solving the dispersive equa tion ut=auxxx.The truncation error of the difference schemes is discussed.Their stability condtitons are introduced as |r|≤3e^(kh)(parameter k≥0,h—space step). As k=0,|r|≤3,the result is much better than |r|≤2.3945 in the litertuers[2] and [3].As k=4,h=π/64,the result is:|r|≤3.6508,whichis 1.5-fold as much as the ressults in[2],[3].