一维非定常对流扩散方程的2m阶指数型高精度差分格式

A h^(2m) Exponential Finite Difference Scheme for the Unsteady One-dimensional Convection-Diffusion Equation

文章对含源项一维非定常对流扩散方程进行分析.对微分方程进行半离散,对半离散后的方程作指数变换消去一阶对流项,构造变换后方程的一种2 m阶(m为任意正整数)的指数型差分格式,作指数变换的逆变换得到原一维非定常对流扩散方程的2 m阶指数型差分格式.分析此格式的稳定性,用数值例子验证提出格式的有效性.

In this paper,we consider the unsteady one-dimensional convection-di ffusion equation with a source term.Firstly,the equation is semi-discreted,and the exponential transform is used to eliminate the one-order convection term.A 2m order(m is arbitrary positive integral)exponential finite difference scheme is developed for this equation after transformed.Then,the inverse transform is used to get the 2m order exponential finite difference for the primitive equatio n.the accuracy of the scheme in this study is higher.The stability is analysised as well.At last,the numerical test shows that the present scheme is effective.