一类对流扩散方程的高精度数值解法

A Class of High Accuracy Numerical Method for Convection Diffusion Equations

本文针对对流扩散方程,建立了一个在空间和时间方向上分别具有四阶和二阶精度的有限差分格式,为了证明解的存在唯一性,建立了一个单调迭代算法,该算法也给出了一个求解算法。

A finite difference method with the accuracies of fourth or second order in time-space is proposed for Convection Diffusion Equation. Then a monotone iterative scheme is developed for proving the existence and uniqueness of the solution of the nonlinear discrete scheme,and the computational algorithms for the periodic solutions are also provided.