{"title":"Besse Extended Cubic B-spline Collocation Method for Solving Benjamin-Bona-Mahony Equation","authors":"Nur Nadiah Mohd Rahan, Nur Nadiah Abd Hamid","doi":"10.11113/matematika.v39.n1.1448","DOIUrl":null,"url":null,"abstract":"Extended cubic B-spline collocation method is formulated to solve the Benjamin-Bona-Mahony equation without linearization. The Besse relaxation scheme is applied on the nonlinear terms and therefore transforms the equation into a systemof two linear equations. The time derivative is discretized using Forward Difference Approximation whereas the spatial dimension is approximated using extended cubic B-spline function. Applying the von-Neumann stability analysis, the proposed technique are shown unconditionally stable. Two numerical examples are presented and the results are compared with the exact solutions and recent methods.","PeriodicalId":43733,"journal":{"name":"Matematika","volume":" ","pages":""},"PeriodicalIF":0.3000,"publicationDate":"2023-04-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Matematika","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.11113/matematika.v39.n1.1448","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0
Abstract
Extended cubic B-spline collocation method is formulated to solve the Benjamin-Bona-Mahony equation without linearization. The Besse relaxation scheme is applied on the nonlinear terms and therefore transforms the equation into a systemof two linear equations. The time derivative is discretized using Forward Difference Approximation whereas the spatial dimension is approximated using extended cubic B-spline function. Applying the von-Neumann stability analysis, the proposed technique are shown unconditionally stable. Two numerical examples are presented and the results are compared with the exact solutions and recent methods.
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