一类非线性偏微分方程的有限差分格式的稳定性研究

数学季刊 ›› 2009, Vol. 24 ›› Issue (3): 394-399.

一类非线性偏微分方程的有限差分格式的稳定性研究

College of Mathematics and Information Science, Henan University

收稿日期:2008-10-23 出版日期:2009-09-30 发布日期:2023-06-29
作者简介: WANG Xiu-qin(1950- ), female, native of Kaifeng, Henan, a professor of Henan University, engages in application mathematics.

The Stability Research of the Finite Difference Scheme for a Nonlinear Partial Differential Equation

College of Mathematics and Information Science, Henan University

Received:2008-10-23 Online:2009-09-30 Published:2023-06-29
About author: WANG Xiu-qin(1950- ), female, native of Kaifeng, Henan, a professor of Henan University, engages in application mathematics.

摘要/Abstract

摘要： The main purpose of this paper is to set up the finite difference scheme with incremental unknowns for the nonlinear differential equation by means of introducing incremental unknowns method and discuss the stability of the scheme. Through the stability analyzing for the scheme, it was shown that the stability of the finite difference scheme with the incremental unknowns is improved when compared with the stability of the corresponding classic difference scheme.

关键词: finite difference, partial differential equation, stability research, incremental
unknowns

Abstract: The main purpose of this paper is to set up the finite difference scheme with incremental unknowns for the nonlinear differential equation by means of introducing incremental unknowns method and discuss the stability of the scheme. Through the stability analyzing for the scheme, it was shown that the stability of the finite difference scheme with the incremental unknowns is improved when compared with the stability of the corresponding classic difference scheme.

Key words: finite difference, partial differential equation, stability research, incremental
unknowns

中图分类号:

O241.84

王秀琴, 徐琛梅. 一类非线性偏微分方程的有限差分格式的稳定性研究[J]. 数学季刊, 2009, 24(3): 394-399.

WANG Xiu-qin, XU Chen-mei. The Stability Research of the Finite Difference Scheme for a Nonlinear Partial Differential Equation[J]. Chinese Quarterly Journal of Mathematics, 2009, 24(3): 394-399.

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[10]	鲁百年, 房少梅. 一维半线性波动方程差分解的收敛性[J]. 数学季刊, 1997, 12(3): 35-40.
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