一种求解双曲方程新的有限差分算法

本文提出一种适于求解一阶双向系统的新的差分格式。它的建立方法是：将所要求解的方程与解的空间导数所满足的微分方程同时离散化，然后再通过插值函数构成封闭的离散变量代数方程。在线性情况下的误差分析表明：该格式的幅值与位相误差均小于常用的一、二阶差分格式；当其应用于非线性气动方程求解时，基本上可以消除数值扩散与振荡这两种非正常现象。

A New Finite-Difference Algorithm forSolving Hyperbolic Equations

This paper present a new finite-difference scheme for solving first-order hyperbolic system. Thescheme is constructed in the way that the discretizations of the differential equations to be solved andthose satisfied by the spatial derivatives of their solutions are made separately at first, and then the al-gebraic equations with respect to the discretization variables are obtained by introducing a proper inter-polation function. The error analysis of a linear system shows that both the phase and amplitude errorsof the algorithm given by the paper are smaller than those of the difference schemes with first and sec-ond order accuracy. In addition, numerical diffusion and oscillation can be eliminated from the solu-tions when the scheme is applied to solving nonlinear gas dynamica equations.