含阻尼项的SRLW方程的一个去耦合线性化差分格式  

A decoupled linearized difference scheme for the SRLW equation with damping term

作　　者：魏杰 何丽 胡劲松 WEI Jie;HE Li;HU Jin-Song(School of Science,Xihua University,Chengdu 610049,China)

机构地区：[1]西华大学理学院,成都610039

出　　处：《四川大学学报（自然科学版）》2020年第5期847-851,共5页Journal of Sichuan University(Natural Science Edition)

基　　金：国家自然科学基金青年基金(11701481);四川省应用基础研究项目(2019YJ0387)。

摘　　要：本文对含阻尼项的耗散SRLW方程的初边值问题进行了数值研究,提出了一个具有二阶理论精度的三层非耦合线性化差分格式.该格式解除了原方程中函数之间的耦合关系,大大提高了求解效率.此外,本文综合运用数学归纳法和离散泛函分析方法证明了格式的收敛性和稳定性.数值实验表明该方法是可靠的.In this paper,a numerical method for initial-boundary value problem of the dissipative SRLW equation with damping term is proposed.A three-level uncoupled linearized difference scheme with second order accuracy is proposed.since the coupling relationship between u andρis removed in this scheme,we can solve the functions uandρrespectively and thus greatly improve the efficiency.While the maximum modulus estimation of the difference solution fails to be obtained,the convergence and stability of the numerical solution are proved directly by inductive method and discrete functional analysis as well.Finally,the efficiency of the scheme is demonstrated by an example.

关 键 词：阻尼耗散 SRLW方程 去耦合 线性化差分格式 收敛性 稳定性 

分 类 号：O241.82[理学—计算数学]