{"title":"孤立波建模的高阶预测校正三次b样条配点法","authors":"Bülent Saka, Ozlem Ersoy Hepson, İdris Dağ","doi":"10.1007/s40010-023-00861-9","DOIUrl":null,"url":null,"abstract":"<div><p>A collocation method with an approximate function consisting of a combination of cubic B-spline functions was established to solve the regularized long wave (RLW) equation. To increase accuracy of the method, multi-step predictor–corrector time integrator is introduced to discretize the RLW equation. The space decomposition of the dependent variable and its derivatives of the RLW equation was accomplished via the B-spline collocation method. Open form of Adams-Bashforth-Moulton method is used as a predictor, then closed Adams-Bashforth-Moulton method is implemented as a corrector. Collocation predictor–corrector method provides an increase in accuracy. Comparison is made with results of some former studies. When high accuracy time discretization is used in getting the solution of the RLW equation, it is observed that the errors are more accurate than the results of the Crank-Nicolson finite element methods listed in the article.</p></div>","PeriodicalId":744,"journal":{"name":"Proceedings of the National Academy of Sciences, India Section A: Physical Sciences","volume":null,"pages":null},"PeriodicalIF":0.8000,"publicationDate":"2023-11-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s40010-023-00861-9.pdf","citationCount":"0","resultStr":"{\"title\":\"High Order Predictor–Corrector Cubic B-Spline Collocation Method for Modeling Solitary Waves\",\"authors\":\"Bülent Saka, Ozlem Ersoy Hepson, İdris Dağ\",\"doi\":\"10.1007/s40010-023-00861-9\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>A collocation method with an approximate function consisting of a combination of cubic B-spline functions was established to solve the regularized long wave (RLW) equation. To increase accuracy of the method, multi-step predictor–corrector time integrator is introduced to discretize the RLW equation. The space decomposition of the dependent variable and its derivatives of the RLW equation was accomplished via the B-spline collocation method. Open form of Adams-Bashforth-Moulton method is used as a predictor, then closed Adams-Bashforth-Moulton method is implemented as a corrector. Collocation predictor–corrector method provides an increase in accuracy. Comparison is made with results of some former studies. When high accuracy time discretization is used in getting the solution of the RLW equation, it is observed that the errors are more accurate than the results of the Crank-Nicolson finite element methods listed in the article.</p></div>\",\"PeriodicalId\":744,\"journal\":{\"name\":\"Proceedings of the National Academy of Sciences, India Section A: Physical Sciences\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.8000,\"publicationDate\":\"2023-11-25\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://link.springer.com/content/pdf/10.1007/s40010-023-00861-9.pdf\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Proceedings of the National Academy of Sciences, India Section A: Physical Sciences\",\"FirstCategoryId\":\"103\",\"ListUrlMain\":\"https://link.springer.com/article/10.1007/s40010-023-00861-9\",\"RegionNum\":4,\"RegionCategory\":\"综合性期刊\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"MULTIDISCIPLINARY SCIENCES\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Proceedings of the National Academy of Sciences, India Section A: Physical Sciences","FirstCategoryId":"103","ListUrlMain":"https://link.springer.com/article/10.1007/s40010-023-00861-9","RegionNum":4,"RegionCategory":"综合性期刊","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MULTIDISCIPLINARY SCIENCES","Score":null,"Total":0}
High Order Predictor–Corrector Cubic B-Spline Collocation Method for Modeling Solitary Waves
A collocation method with an approximate function consisting of a combination of cubic B-spline functions was established to solve the regularized long wave (RLW) equation. To increase accuracy of the method, multi-step predictor–corrector time integrator is introduced to discretize the RLW equation. The space decomposition of the dependent variable and its derivatives of the RLW equation was accomplished via the B-spline collocation method. Open form of Adams-Bashforth-Moulton method is used as a predictor, then closed Adams-Bashforth-Moulton method is implemented as a corrector. Collocation predictor–corrector method provides an increase in accuracy. Comparison is made with results of some former studies. When high accuracy time discretization is used in getting the solution of the RLW equation, it is observed that the errors are more accurate than the results of the Crank-Nicolson finite element methods listed in the article.
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