{"title":"A novel explicit fully-discrete momentum-preserving scheme of damped nonlinear stochastic wave equation influenced by multiplicative space-time noise","authors":"Feng Wang, Zhenyu Wang, Qiang Ma, Xiaohua Ding","doi":"10.1016/j.aml.2024.109325","DOIUrl":null,"url":null,"abstract":"<div><div>In this paper, the evolution laws of global momentum and averaged global momentum for the damped nonlinear stochastic wave equation (DNSWE) influenced by multiplicative space-time noise are derived. We innovatively combine the second-order central finite difference method and discrete gradient method in space, and integrate the splitting method and Störmer-Verlet type method in time. Both the novel spatial semi-discrete scheme and fully-discrete scheme constructed in this way can successfully preserve the corresponding evolution laws for discrete global momentum and discrete averaged global momentum. Numerical experiments on DNSWE with cubic nonlinearity validate the theoretical results.</div></div>","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":"160 ","pages":"Article 109325"},"PeriodicalIF":2.9000,"publicationDate":"2024-09-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Applied Mathematics Letters","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0893965924003458","RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
引用次数: 0
Abstract
In this paper, the evolution laws of global momentum and averaged global momentum for the damped nonlinear stochastic wave equation (DNSWE) influenced by multiplicative space-time noise are derived. We innovatively combine the second-order central finite difference method and discrete gradient method in space, and integrate the splitting method and Störmer-Verlet type method in time. Both the novel spatial semi-discrete scheme and fully-discrete scheme constructed in this way can successfully preserve the corresponding evolution laws for discrete global momentum and discrete averaged global momentum. Numerical experiments on DNSWE with cubic nonlinearity validate the theoretical results.
期刊介绍：
The purpose of Applied Mathematics Letters is to provide a means of rapid publication for important but brief applied mathematical papers. The brief descriptions of any work involving a novel application or utilization of mathematics, or a development in the methodology of applied mathematics is a potential contribution for this journal. This journal''s focus is on applied mathematics topics based on differential equations and linear algebra. Priority will be given to submissions that are likely to appeal to a wide audience.
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