{"title":"A radial basis function (RBF)-finite difference method for solving improved Boussinesq model with error estimation and description of solitary waves","authors":"Mostafa Abbaszadeh, AliReza Bagheri Salec, Taghreed Abdul-Kareem Hatim Aal-Ezirej","doi":"10.1002/num.23077","DOIUrl":null,"url":null,"abstract":"The Boussinesq equation has some application in fluid dynamics, water sciences and so forth. In the current paper, we study an improved Boussinesq model. First, a finite difference approximation is employed to discrete the derivative of the temporal variable. Then, we study the existence and uniqueness of solution of the semi-discrete scheme according to the fixed point theorem. In addition, the unconditional stability and convergence of the semi-discrete scheme are presented. Then, we construct the fully discrete formulation based upon the radial basis function-finite difference method. The convergence rate and stability of the fully-discrete scheme are analyzed. In the end, some examples in 1D and 2D cases are studied to corroborate the capability of the proposed scheme.","PeriodicalId":19443,"journal":{"name":"Numerical Methods for Partial Differential Equations","volume":"53 1","pages":""},"PeriodicalIF":2.1000,"publicationDate":"2023-11-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Numerical Methods for Partial Differential Equations","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1002/num.23077","RegionNum":3,"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
The Boussinesq equation has some application in fluid dynamics, water sciences and so forth. In the current paper, we study an improved Boussinesq model. First, a finite difference approximation is employed to discrete the derivative of the temporal variable. Then, we study the existence and uniqueness of solution of the semi-discrete scheme according to the fixed point theorem. In addition, the unconditional stability and convergence of the semi-discrete scheme are presented. Then, we construct the fully discrete formulation based upon the radial basis function-finite difference method. The convergence rate and stability of the fully-discrete scheme are analyzed. In the end, some examples in 1D and 2D cases are studied to corroborate the capability of the proposed scheme.
期刊介绍：
An international journal that aims to cover research into the development and analysis of new methods for the numerical solution of partial differential equations, it is intended that it be readily readable by and directed to a broad spectrum of researchers into numerical methods for partial differential equations throughout science and engineering. The numerical methods and techniques themselves are emphasized rather than the specific applications. The Journal seeks to be interdisciplinary, while retaining the common thread of applied numerical analysis.
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