解中立型时滞抛物方程的隐式差分格式

J4 ›› 2011, Vol. 46 ›› Issue (8): 13-16.

解中立型时滞抛物方程的隐式差分格式

金承日,于战华,曲荣宁

哈尔滨工业大学(威海)数学系, 山东威海 264209

收稿日期:2010-04-05 出版日期:2011-08-20 发布日期:2011-09-08
作者简介:金承日(1961- ),男,博士,教授,研究方向为偏微分方程数值分析.Email:jincr0327@163.com
基金资助:
哈尔滨工业大学(威海)校研究基金资助项目(HIT(WH)200706)

An implicit difference scheme for solving the neutral delay parabolic differential equation

JIN Cheng-ri, YU Zhan-hua, QU Rong-ning

Department of Mathematics, Harbin Institute of Technology at Weihai, Weihai 264209, Shandong,China

Received:2010-04-05 Online:2011-08-20 Published:2011-09-08

摘要/Abstract

摘要：

构造了求解中立型时滞抛物方程的一个隐式差分格式,该格式在离散L2范数意义下是无条件稳定的,局部截断误差阶为O(Δt²+Δx²)。该格式在每一个时间层上可以化为三对角线性方程组,用追赶法很容易求解。数值算例表明该差分格式是有效的。

关键词: 中立型时滞抛物方程;隐式差分格式;无条件稳定

Abstract:

An implicit difference scheme for solving the neutral delay parabolic differential equation is presented. This scheme is unconditional stable in the sense of discrete L2norm. The local truncation error of this scheme is O(Δt²+Δx²). This scheme leads to a tridiagonal linear system to be solved at each time-step. The Crout factorization algorithm is used to solve this linear system. The numerical results show that the presented implicit difference scheme is effective.

Key words: neutral delay parabolic differential equation; implicit difference scheme; unconditional stable

金承日,于战华,曲荣宁. 解中立型时滞抛物方程的隐式差分格式[J]. J4, 2011, 46(8): 13-16.

JIN Cheng-ri, YU Zhan-hua, QU Rong-ning. An implicit difference scheme for solving the neutral delay parabolic differential equation[J]. J4, 2011, 46(8): 13-16.

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