发展方程的稳定性分析

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翻新时间：2023-08-07

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发展方程的稳定性分析

摘要

本论文主要是对发展方程差分方法的稳定性进行讨论。首先介绍了3类发展方程 (扩散方程、波动方程、对流扩散方程)，然后介绍了扩散方程的差分法与3种计算格式，接着介绍了用来研究发展方程差分方法的稳定性分析的4种方法：①直接法，② 分离变量法，③最大模方法，④传播因子法。论文最后还进行了实例分析，并对计算结果进行了相应的讨论。

关键词：发展方程；差分方法；稳定性；计算格式；收敛性；Lax等价原理；差分格式；初值问题；

Abstract

In this paper we mainly discuss the stability of difference method of the development equation. First of all we introduce three types of development equation. They are diffusion equation, wave equation and convection-diffusion equation. And at the same time we introduce the difference method of diffusion equation and three kinds of computational scheme. There are four methods which are used to study the stability of difference method of the development equation. The first is direct method, the second is separation of variables, the third is The Largest-scale method, The fourth is transmission factor method. We also introduce case study in the end of this paper and analysis the result of the computation accordingly.

Keywords: development equation; difference method; stability; computational scheme; convergence; Lax equivalence principle; difference scheme; initial problems