求解偏微分方程的格点法

格点法是在计算流体力学中首先发展起来的数值模拟新方法，共根本思想是对问题重新建模，建立直接模拟流体运动的离散格点模型。本文以一阶拟线性双典型方程及Ｋｄｖ方程为例，推广这种求解一般偏微分方程的。它是运用多尺度分析方法，构造出格点模型的演化方程的局部平衡分布函数。数值试验表明，该方法程序实现简单，求解速度快，数值结果令人满意。

Lattice Method for Solving Partial Differential Equations

,The lattice method is a new numerical simulation method which is firstly developed from computation fluid dynamics. Its essential idea is to rebuild its model for mathematical physical problems, and establish the disperse lattice model for simulating fluid movement directly. This paper takes the first order simulation linear double typical equation and Kdv equation as examples, and tries to spread this method for solving general partial differential equation. The local equilibrium distribution function of lattice model evolution equation is constructed by use of multi scale analysis.The numerical testing shows that the method has simple computer program and satisfactory result with fast solution speed.