{"title":"Numerical simulation of the generalized modified Benjamin–Bona–Mahony equation using SBP-SAT in time","authors":"Vilma Kjelldahl, Ken Mattsson","doi":"10.1016/j.cam.2024.116377","DOIUrl":null,"url":null,"abstract":"<div><div>In this paper we present high-order accurate finite difference approximations for solving the generalized modified Benjamin–Bona–Mahony (BBM) equation, a non-linear soliton model. The spatial discretization uses high-order accurate summation-by-parts (SBP) finite difference operators combined with both weak and strong enforcement of boundary conditions. For time integration we compare the explicit RK4 method against an implicit SBP time integrator. These time-marching methods are evaluated and compared in terms of accuracy and efficiency. It is shown that the implicit SBP time-integrator is more efficient than the explicit RK4 method for non-linear soliton models.</div></div>","PeriodicalId":50226,"journal":{"name":"Journal of Computational and Applied Mathematics","volume":"459 ","pages":"Article 116377"},"PeriodicalIF":2.1000,"publicationDate":"2024-11-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Computational and Applied Mathematics","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0377042724006253","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 we present high-order accurate finite difference approximations for solving the generalized modified Benjamin–Bona–Mahony (BBM) equation, a non-linear soliton model. The spatial discretization uses high-order accurate summation-by-parts (SBP) finite difference operators combined with both weak and strong enforcement of boundary conditions. For time integration we compare the explicit RK4 method against an implicit SBP time integrator. These time-marching methods are evaluated and compared in terms of accuracy and efficiency. It is shown that the implicit SBP time-integrator is more efficient than the explicit RK4 method for non-linear soliton models.
期刊介绍：
The Journal of Computational and Applied Mathematics publishes original papers of high scientific value in all areas of computational and applied mathematics. The main interest of the Journal is in papers that describe and analyze new computational techniques for solving scientific or engineering problems. Also the improved analysis, including the effectiveness and applicability, of existing methods and algorithms is of importance. The computational efficiency (e.g. the convergence, stability, accuracy, ...) should be proved and illustrated by nontrivial numerical examples. Papers describing only variants of existing methods, without adding significant new computational properties are not of interest.
The audience consists of: applied mathematicians, numerical analysts, computational scientists and engineers.
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