改进的线性传输方程满足两个守恒律的非线性差分格式  

THE IMPROVED NONLINEAR DIFFERENCE SCHEME FOR THE LINEAR TRANSMISSION EQUATION WHICH SATISFIES TWO CONSERVATION LAWS

作　　者：刘小妮 崔艳芬[1] 王志刚[2] Liu Xiaoni;Cui Yanfen;Wang Zhigang(College of Sciences,Shanghai University,Shanghai 200444;Fuyang Normal University,Anhui 236037)

机构地区：[1]上海大学理学院,上海200444 [2]阜阳师范学院,安徽236037

出　　处：《高等学校计算数学学报》2022年第3期203-215,共13页Numerical Mathematics A Journal of Chinese Universities

基　　金：国家自然科学基金资助项目(12171308);安徽省高校领军人才引进与培育计划项目(gxfxZD2016170);安徽高校省级科学研究重点项目(KJ2019A0530)。

摘　　要：1引言近年来,文献[1,2,3,5,6,7]和[8],对发展型偏微分方程设计了一种能保持多个相关离散守恒律的差分方法,这类数值方法在长时间的数值模拟中,表现出更好的保结构性质.其中[3,5,6]对双曲型方程(组)设计了一类满足两个守恒律的熵耗散格式,数值试验表明这类格式具有更好的稳定性;[7]和[8]对线性方程(组)以及变系数的一阶方程,设计了满足多个守恒律的数值方法,从数值结果可以看出满足的守恒律越多。The references[2,7]and[8]design a numerical method for the linear transmission equation that satisfies multiple discrete conservation laws.This kind of numerical method shows excellent properties in the precision of solution and long-time numerical simulation.In this paper,a kind of improved method to satisfy two conservation laws for linear transmission equations is designed,which is different from the scheme in[2].In this paper,the numerical flow is evolved by numerical method in the time direction,so that the scheme is more universal,and the error accumulation feature of the scheme is analyzed.It shows that the error of the scheme is self-canceling,so it’s super-convergence.

关 键 词：守恒律 偏微分方程 差分方法 双曲型 数值方法 变系数 数值试验 

分 类 号：TP391.00[自动化与计算机技术—计算机应用技术]