Extended modified cubic B-spline algorithm for nonlinear Burgers' equation
In this paper, an extended modified cubic B-Spline differential quadrature method is proposed to approximate the solution of the nonlinear Burgers' equation. The proposed method is used in space and a five-stage and four order strong stability-preserving time-stepping Runge–Kutta (SSP-RK54) met...
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| Format: | Article |
| Language: | English |
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SpringerOpen
2016-09-01
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| Series: | Beni-Suef University Journal of Basic and Applied Sciences |
| Subjects: | |
| Online Access: | http://www.sciencedirect.com/science/article/pii/S2314853516300646 |
| _version_ | 1811291542427533312 |
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| author | Mohammad Tamsir Neeraj Dhiman Vineet K. Srivastava |
| author_facet | Mohammad Tamsir Neeraj Dhiman Vineet K. Srivastava |
| author_sort | Mohammad Tamsir |
| collection | DOAJ |
| description | In this paper, an extended modified cubic B-Spline differential quadrature method is proposed to approximate the solution of the nonlinear Burgers' equation. The proposed method is used in space and a five-stage and four order strong stability-preserving time-stepping Runge–Kutta (SSP-RK54) method is used in time. The accuracy and efficiency of the method is illustrated by considering four numerical problems. The numerical results of the method are compared with some existing methods and it was found that the proposed numerical method produces acceptable results and even more accurate results in comparison with some existing methods. The stability analysis of the scheme is also carried out and was found to be unconditionally stable. |
| first_indexed | 2024-04-13T04:30:57Z |
| format | Article |
| id | doaj.art-f93c051563fd4ad984277f19d73fe744 |
| institution | Directory Open Access Journal |
| issn | 2314-8535 |
| language | English |
| last_indexed | 2024-04-13T04:30:57Z |
| publishDate | 2016-09-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Beni-Suef University Journal of Basic and Applied Sciences |
| spelling | doaj.art-f93c051563fd4ad984277f19d73fe7442022-12-22T03:02:19ZengSpringerOpenBeni-Suef University Journal of Basic and Applied Sciences2314-85352016-09-015324425410.1016/j.bjbas.2016.09.001Extended modified cubic B-spline algorithm for nonlinear Burgers' equationMohammad Tamsir0Neeraj Dhiman1Vineet K. Srivastava2Department of Mathematics, Graphic Era University, Dehradun 248001, IndiaDepartment of Mathematics, Graphic Era University, Dehradun 248001, IndiaFlight Dynamics Group, ISRO Telemetry Tracking and Command Network, Bangalore 560058, IndiaIn this paper, an extended modified cubic B-Spline differential quadrature method is proposed to approximate the solution of the nonlinear Burgers' equation. The proposed method is used in space and a five-stage and four order strong stability-preserving time-stepping Runge–Kutta (SSP-RK54) method is used in time. The accuracy and efficiency of the method is illustrated by considering four numerical problems. The numerical results of the method are compared with some existing methods and it was found that the proposed numerical method produces acceptable results and even more accurate results in comparison with some existing methods. The stability analysis of the scheme is also carried out and was found to be unconditionally stable.http://www.sciencedirect.com/science/article/pii/S2314853516300646Extended modified cubic B-spline functionsDQMBurgers' equationSSP-RK54Stability analysis |
| spellingShingle | Mohammad Tamsir Neeraj Dhiman Vineet K. Srivastava Extended modified cubic B-spline algorithm for nonlinear Burgers' equation Beni-Suef University Journal of Basic and Applied Sciences Extended modified cubic B-spline functions DQM Burgers' equation SSP-RK54 Stability analysis |
| title | Extended modified cubic B-spline algorithm for nonlinear Burgers' equation |
| title_full | Extended modified cubic B-spline algorithm for nonlinear Burgers' equation |
| title_fullStr | Extended modified cubic B-spline algorithm for nonlinear Burgers' equation |
| title_full_unstemmed | Extended modified cubic B-spline algorithm for nonlinear Burgers' equation |
| title_short | Extended modified cubic B-spline algorithm for nonlinear Burgers' equation |
| title_sort | extended modified cubic b spline algorithm for nonlinear burgers equation |
| topic | Extended modified cubic B-spline functions DQM Burgers' equation SSP-RK54 Stability analysis |
| url | http://www.sciencedirect.com/science/article/pii/S2314853516300646 |
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