求解对流扩散方程的一种有限分析方法

A KIND OF FINITE ANALYTIC METHODS FOR SOLVING CONVECTION-DIFFUSION EQUATIONS

本文提出了一种求解线性与拟线性对流扩散方程的有限分析格式,证明了这种格式的解的存在唯一性及绝对稳定性与广义弱稳定性等,大量算例表明它具有较高的精度与很好的稳定性。

In this paper a kind of Finite Analytic Methods is derived and applied on convection -diffusion equations. These qualities proved are existence, uniqueness, absolute stability and convergence of solutions of finite analytic scheme of linear equations, so are existence, uniqueness and generalized weak stabability of solutions of finite analytic scheme of Burger's equation. Numerical experiments show that the finite analytic scheme is very effective, especially numerical solutions arc not oscillating.