A SINGULAR PERTURBATION PROBLEM FOR PERIODIC BOUNDARY DIFFERENTIAL EQUATION

In this paper, we consider a second order ordinary differential equation with a small,positive parameter ε in its highest derivative for periodic boundary values problem andprove that the solution of difference scheme in paper [1] uniformly converges to the solutionof its original problem with order one.     

A singular perturbation problem for periodic boundary partial differential equation

In this paper,we consider a singular perturbation elliptic-parabolic partial differentialequation for periodic boundary value problem,and construct a difference scheme.Using themethod of decomposing the singular term from its solution and combining an asymptoticexpansion of the equation,we prove that the scheme constructed by this paper convergesuniformly to the solution of its original problem with O(τ h~2).     

奇异摄动的周期边界问题

本文讨论高阶导数项含小参数ε的二阶常微分方程的周期边界问题。证明了文[1]差分格式具有O(h)一致收敛阶。     

Poisson方程的快速直接解法

既简便又可节省大量的存贮单元。但遗憾的是他没有具体给出P的形式,从而也就没有指出M_1、M_2的形式,以便进一步快速求解。 本文找到一种将网格结点排序编号的办法,也就是找到一种特殊置换使A,B很有规则,即A,B具有特殊结构,这时可用熟知的直接法如Fourier分析法进一步求解     

A singular perturbation problem for periodic boundary differential equation

In this paper, we consider a second order ordinary differential equation with a small, positive parameter ε in its highest derivative for periodic boundary values problem and prove that the solution of difference scheme in paper [1] uniformly converges to the solution of its original problem with order one.