解对流扩散方程的四阶耗散的单侧逼近指数型格式

A FOURTH-ORDER DISSIPATION EXPONENT-TYPE SCHEME OF ONE-SIDED APPROXIMATION FOR SOLVING CONVECTIVE DIFFUSION EQUATIONS

本文构造了一种带权的六点格式,讨论了它的稳定性条件,证明了这种格式的解对微分方程的真解具有单侧逼近的性质;当适当选取权数θ=θ_0时,这种格式是一种四阶耗散格式,不仅数值耗散很小,而且满足稳定性条件,不出现非物理振荡;还证明了C.J.Chen的有限分析格式在一定条件下是这种带权格式的一个特殊情形,因此也具有单侧逼近性质;最后给出了几个算例说明上述性质。

In this paper a fourth -oder dissipation exponent- type scheme of one -sided approximation for solving convective diffusion equations is derived. The theoretical results on the stability and the properties of one -sided approximation and fourth -oder dissipation of this scheme have been presented. The relations of this scheme and finite analytic method is also obtained. Some numerical examples are qiven.