{"title":"求解Benjamin-Bona-Mahony方程的Besse扩展三次B样条配置方法","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":null,"pages":null},"PeriodicalIF":0.3000,"publicationDate":"2023-04-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"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\":null,\"pages\":null},\"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}","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}
Besse Extended Cubic B-spline Collocation Method for Solving Benjamin-Bona-Mahony Equation
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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