{"title":"基于五次b样条的时间分数型Kuramoto-Sivashinsky方程的改进Atangana-Baleanu Caputo算子","authors":"Komal Deswal, Renu Choudhary, Devendra Kumar","doi":"10.1115/1.4063554","DOIUrl":null,"url":null,"abstract":"Abstract A novel numerical scheme for the time-fractional Kuramoto-Sivashinsky equation is presented in this article. A modification of the Atangana-Baleanu Caputo derivative known as the modified Atangana-Baleanu Caputo operator is introduced for the time-fractional derivative. A Taylor series-based formula is used to derive a second-order accurate approximation to the modified Atangana-Baleanu Caputo derivative. A linear combination of the quintic $B$-spline basis functions is used to approximate the functions in spatial direction. Moreover, through rigorous analysis, it has been proved that the present scheme is unconditionally stable and convergent. Finally, two test problems are solved numerically to demonstrate the proposed method's superconvergence and accuracy.","PeriodicalId":54858,"journal":{"name":"Journal of Computational and Nonlinear Dynamics","volume":"54 1","pages":"0"},"PeriodicalIF":1.9000,"publicationDate":"2023-09-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Modified Atangana-Baleanu Caputo Operator for Time-Fractional Kuramoto-Sivashinsky Equation via Quintic B-Splines\",\"authors\":\"Komal Deswal, Renu Choudhary, Devendra Kumar\",\"doi\":\"10.1115/1.4063554\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Abstract A novel numerical scheme for the time-fractional Kuramoto-Sivashinsky equation is presented in this article. A modification of the Atangana-Baleanu Caputo derivative known as the modified Atangana-Baleanu Caputo operator is introduced for the time-fractional derivative. A Taylor series-based formula is used to derive a second-order accurate approximation to the modified Atangana-Baleanu Caputo derivative. A linear combination of the quintic $B$-spline basis functions is used to approximate the functions in spatial direction. Moreover, through rigorous analysis, it has been proved that the present scheme is unconditionally stable and convergent. Finally, two test problems are solved numerically to demonstrate the proposed method's superconvergence and accuracy.\",\"PeriodicalId\":54858,\"journal\":{\"name\":\"Journal of Computational and Nonlinear Dynamics\",\"volume\":\"54 1\",\"pages\":\"0\"},\"PeriodicalIF\":1.9000,\"publicationDate\":\"2023-09-29\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Journal of Computational and Nonlinear Dynamics\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1115/1.4063554\",\"RegionNum\":4,\"RegionCategory\":\"工程技术\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"ENGINEERING, MECHANICAL\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Computational and Nonlinear Dynamics","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1115/1.4063554","RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"ENGINEERING, MECHANICAL","Score":null,"Total":0}
Modified Atangana-Baleanu Caputo Operator for Time-Fractional Kuramoto-Sivashinsky Equation via Quintic B-Splines
Abstract A novel numerical scheme for the time-fractional Kuramoto-Sivashinsky equation is presented in this article. A modification of the Atangana-Baleanu Caputo derivative known as the modified Atangana-Baleanu Caputo operator is introduced for the time-fractional derivative. A Taylor series-based formula is used to derive a second-order accurate approximation to the modified Atangana-Baleanu Caputo derivative. A linear combination of the quintic $B$-spline basis functions is used to approximate the functions in spatial direction. Moreover, through rigorous analysis, it has been proved that the present scheme is unconditionally stable and convergent. Finally, two test problems are solved numerically to demonstrate the proposed method's superconvergence and accuracy.
期刊介绍:
The purpose of the Journal of Computational and Nonlinear Dynamics is to provide a medium for rapid dissemination of original research results in theoretical as well as applied computational and nonlinear dynamics. The journal serves as a forum for the exchange of new ideas and applications in computational, rigid and flexible multi-body system dynamics and all aspects (analytical, numerical, and experimental) of dynamics associated with nonlinear systems. The broad scope of the journal encompasses all computational and nonlinear problems occurring in aeronautical, biological, electrical, mechanical, physical, and structural systems.