双曲方程的高稳定性蛙跳格式

A LEAP-FROG FINITE DIFFERENCE SCHEME WITH HIGHER STABILITY PROPERTIES FOR HYPERBOLIC EQUATIONS

本文提出了一种数值求解双曲方程Ut+aUx=0的高稳定性蛙跳显格式。文中格式的局部截断误差为O（τ2＋h2），而稳定性条件为|R|≤g（β）（其中g对任意正实数是单调递增函数），是同类格式中最好的。

A clase of leap-frog finite difference scheme with higher stability propertiesfor a hyperbolic equation Ut+aUx=0 are proposed in this paper. Their local trunction errors are 0 (τ2+h2) and stability conditions are |R|≤g(β), where g is an increasing functionof its variable. The stability conditions seem to be the best for schemes of the same type atpresent.