A finite difference method for Burgers' equation in the unbounded domain using artificial boundary conditions

被引：0

作者：

Zheng, Quan ^{[1
]}

Liu, Yufeng ^{[1
]}

Fan, Lei ^{[1
]}

机构：

[1] North China Univ Technol, Coll Sci, Beijing 100144, Peoples R China

来源：

JOURNAL OF COMPUTATIONAL ANALYSIS AND APPLICATIONS | 2016年 / 20卷 / 01期

基金：

中国国家自然科学基金;

关键词：

Burgers' equation; infinite domain; Hopf-Cole transformation; Artificial boundary condition; Finite difference method; HEAT-EQUATION;

D O I：

暂无

中图分类号：

TP301 [理论、方法];

学科分类号：

081202 ;

摘要：

This paper discusses the numerical solution of one-dimensional Burgers' equation in the infinite domain. The original problem is converted by Hopf-Cole transformation to the heat equation in the infinite domain, the latter is reduced to an equivalent problem in a finite computational domain with two artificial integral boundary conditions, a finite difference method is constructed for last problem by the method of reduction of order, and therefore the numerical solution of Burgers' equation is obtained. The method is proved and verified to be uniquely solvable, unconditionally stable and convergent with the order 2 in space and the order 3/2 in time for solving the heat equation as well as Burgers' equation in the computational domain.

引用

页码：140 / 150

页数：11

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