Numerical Simulation of Time Fractional BBM-Burger Equation Using Cubic B-Spline Functions
The unidirectional propagation of long waves in certain nonlinear dispersive system is explained by the Benjamin-Bona-Mahony-Burger (BBM-Burger) equation. The purpose of this study is to investigate the BBM-Burger equation numerically using Caputo derivative and B-spline basis functions. The fractio...
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| Main Authors: | , , , , |
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| Format: | Article |
| Language: | English |
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Wiley
2022-01-01
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| Series: | Journal of Function Spaces |
| Online Access: | http://dx.doi.org/10.1155/2022/2119416 |
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| author | Mohsin Kamran Muhammad Abbas Abdul Majeed Homan Emadifar Tahir Nazir |
| author_facet | Mohsin Kamran Muhammad Abbas Abdul Majeed Homan Emadifar Tahir Nazir |
| author_sort | Mohsin Kamran |
| collection | DOAJ |
| description | The unidirectional propagation of long waves in certain nonlinear dispersive system is explained by the Benjamin-Bona-Mahony-Burger (BBM-Burger) equation. The purpose of this study is to investigate the BBM-Burger equation numerically using Caputo derivative and B-spline basis functions. The fractional derivative is considered in Caputo form, and L1 formula is used for discretization of temporal derivative. The interpolation of space derivative is done with the help of B-spline functions. The effect of α and time on solution profile of travelling wave for different domain of x is discussed in this paper. The numerical results have been presented to show that the cubic B-spline method is effective and efficient in solving the time fractional Benjamin-Bona-Mahony-Burger (BBM-Burger) equation. Moreover, the convergence and stability of the proposed scheme are analyzed. The error norms are also calculated to check the accuracy of the proposed scheme. The numerical results reflect that the proposed scheme can be used for linear and highly nonlinear models. |
| format | Article |
| id | doaj-art-b1ca5485d5064a21bccf24e4520d44b9 |
| institution | Kabale University |
| issn | 2314-8888 |
| language | English |
| publishDate | 2022-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Function Spaces |
| spelling | doaj-art-b1ca5485d5064a21bccf24e4520d44b92025-02-03T01:00:14ZengWileyJournal of Function Spaces2314-88882022-01-01202210.1155/2022/2119416Numerical Simulation of Time Fractional BBM-Burger Equation Using Cubic B-Spline FunctionsMohsin Kamran0Muhammad Abbas1Abdul Majeed2Homan Emadifar3Tahir Nazir4Department of MathematicsDepartment of MathematicsDepartment of MathematicsDepartment of MathematicsDepartment of MathematicsThe unidirectional propagation of long waves in certain nonlinear dispersive system is explained by the Benjamin-Bona-Mahony-Burger (BBM-Burger) equation. The purpose of this study is to investigate the BBM-Burger equation numerically using Caputo derivative and B-spline basis functions. The fractional derivative is considered in Caputo form, and L1 formula is used for discretization of temporal derivative. The interpolation of space derivative is done with the help of B-spline functions. The effect of α and time on solution profile of travelling wave for different domain of x is discussed in this paper. The numerical results have been presented to show that the cubic B-spline method is effective and efficient in solving the time fractional Benjamin-Bona-Mahony-Burger (BBM-Burger) equation. Moreover, the convergence and stability of the proposed scheme are analyzed. The error norms are also calculated to check the accuracy of the proposed scheme. The numerical results reflect that the proposed scheme can be used for linear and highly nonlinear models.http://dx.doi.org/10.1155/2022/2119416 |
| spellingShingle | Mohsin Kamran Muhammad Abbas Abdul Majeed Homan Emadifar Tahir Nazir Numerical Simulation of Time Fractional BBM-Burger Equation Using Cubic B-Spline Functions Journal of Function Spaces |
| title | Numerical Simulation of Time Fractional BBM-Burger Equation Using Cubic B-Spline Functions |
| title_full | Numerical Simulation of Time Fractional BBM-Burger Equation Using Cubic B-Spline Functions |
| title_fullStr | Numerical Simulation of Time Fractional BBM-Burger Equation Using Cubic B-Spline Functions |
| title_full_unstemmed | Numerical Simulation of Time Fractional BBM-Burger Equation Using Cubic B-Spline Functions |
| title_short | Numerical Simulation of Time Fractional BBM-Burger Equation Using Cubic B-Spline Functions |
| title_sort | numerical simulation of time fractional bbm burger equation using cubic b spline functions |
| url | http://dx.doi.org/10.1155/2022/2119416 |
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