{"title":"非局部波方程的线性隐式和能量守恒方案的无条件误差估计","authors":"Lingling Li , Yayun Fu","doi":"10.1016/j.camwa.2024.11.002","DOIUrl":null,"url":null,"abstract":"<div><div>Compared to the classical wave equation, the nonlocal wave equation incorporates a nonlocal operator and can capture a broader range of practical phenomena. However, this nonlocal formulation significantly increases the computational cost in numerical simulations, necessitating the development of efficient and accurate time integration schemes. Inspired by the newly developed generalized scalar auxiliary variable (GSAV) method in Refs. <span><span>[8]</span></span>, <span><span>[24]</span></span> for dissipative systems, this paper uses the GSAV approach to construct linearly-implicit energy-preserving schemes for nonlocal wave systems. The developed numerical schemes only require solving linear equations with constant coefficients at each time step and are more efficient than the original SAV schemes <span><span>[30]</span></span> for wave equations. We also discuss the unique solvability, conduct a rigorous error analysis, and present numerical examples to demonstrate the accuracy, conservation and effectiveness of the obtained schemes.</div></div>","PeriodicalId":55218,"journal":{"name":"Computers & Mathematics with Applications","volume":"176 ","pages":"Pages 492-509"},"PeriodicalIF":2.9000,"publicationDate":"2024-11-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Unconditional error estimate of linearly-implicit and energy-preserving schemes for nonlocal wave equations\",\"authors\":\"Lingling Li , Yayun Fu\",\"doi\":\"10.1016/j.camwa.2024.11.002\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><div>Compared to the classical wave equation, the nonlocal wave equation incorporates a nonlocal operator and can capture a broader range of practical phenomena. However, this nonlocal formulation significantly increases the computational cost in numerical simulations, necessitating the development of efficient and accurate time integration schemes. Inspired by the newly developed generalized scalar auxiliary variable (GSAV) method in Refs. <span><span>[8]</span></span>, <span><span>[24]</span></span> for dissipative systems, this paper uses the GSAV approach to construct linearly-implicit energy-preserving schemes for nonlocal wave systems. The developed numerical schemes only require solving linear equations with constant coefficients at each time step and are more efficient than the original SAV schemes <span><span>[30]</span></span> for wave equations. We also discuss the unique solvability, conduct a rigorous error analysis, and present numerical examples to demonstrate the accuracy, conservation and effectiveness of the obtained schemes.</div></div>\",\"PeriodicalId\":55218,\"journal\":{\"name\":\"Computers & Mathematics with Applications\",\"volume\":\"176 \",\"pages\":\"Pages 492-509\"},\"PeriodicalIF\":2.9000,\"publicationDate\":\"2024-11-13\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Computers & Mathematics with Applications\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://www.sciencedirect.com/science/article/pii/S0898122124004930\",\"RegionNum\":2,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"MATHEMATICS, APPLIED\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Computers & Mathematics with Applications","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0898122124004930","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
摘要
与经典波方程相比,非局部波方程包含一个非局部算子,可以捕捉更广泛的实际现象。然而,这种非局部公式大大增加了数值模拟的计算成本,因此必须开发高效、精确的时间积分方案。受文献[8]、[24]中针对耗散系统新开发的广义标量辅助变量(GSAV)方法的启发,本文利用 GSAV 方法构建了非局部波系统的线性隐式能量守恒方案。所开发的数值方案只需在每个时间步求解具有常数系数的线性方程组,比最初的 SAV 方案 [30] 更有效地求解波方程。我们还讨论了独特的可解性,进行了严格的误差分析,并给出了数值示例,以证明所获方案的准确性、守恒性和有效性。
Unconditional error estimate of linearly-implicit and energy-preserving schemes for nonlocal wave equations
Compared to the classical wave equation, the nonlocal wave equation incorporates a nonlocal operator and can capture a broader range of practical phenomena. However, this nonlocal formulation significantly increases the computational cost in numerical simulations, necessitating the development of efficient and accurate time integration schemes. Inspired by the newly developed generalized scalar auxiliary variable (GSAV) method in Refs. [8], [24] for dissipative systems, this paper uses the GSAV approach to construct linearly-implicit energy-preserving schemes for nonlocal wave systems. The developed numerical schemes only require solving linear equations with constant coefficients at each time step and are more efficient than the original SAV schemes [30] for wave equations. We also discuss the unique solvability, conduct a rigorous error analysis, and present numerical examples to demonstrate the accuracy, conservation and effectiveness of the obtained schemes.
期刊介绍:
Computers & Mathematics with Applications provides a medium of exchange for those engaged in fields contributing to building successful simulations for science and engineering using Partial Differential Equations (PDEs).