Numerical simulation for an initial-boundary value problem of time-fractional Klein-Gordon equations
This paper mainly presents numerical solutions to an initial-boundary value problem of the time-fractional Klein-Gordon equations. We developed a numerical scheme with the help of the finite difference methods and the predictor-corrector methods to find numerical solutions of the considered problems...
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| Published in | Applied numerical mathematics Vol. 206; pp. 1 - 11 |
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| Main Author | |
| Format | Journal Article |
| Language | English |
| Published |
Elsevier B.V
01.12.2024
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| Subjects | |
| Online Access | Get full text |
| ISSN | 0168-9274 |
| DOI | 10.1016/j.apnum.2024.07.015 |
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| Abstract | This paper mainly presents numerical solutions to an initial-boundary value problem of the time-fractional Klein-Gordon equations. We developed a numerical scheme with the help of the finite difference methods and the predictor-corrector methods to find numerical solutions of the considered problems. The proposed scheme is based on discretizing the considered problems with respect to spatial and temporal domains. Numerical results are derived for some illustrative problems, and the outputs are compared with the exact solution in the integer order case. The solution behavior and 3D graphics of the discussed problems are demonstrated using the proposed scheme. Finally, the proposed scheme, which does not require solving large systems of linear equations, can be extended and modified to handle other classes of time-fractional PDEs. |
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| AbstractList | This paper mainly presents numerical solutions to an initial-boundary value problem of the time-fractional Klein-Gordon equations. We developed a numerical scheme with the help of the finite difference methods and the predictor-corrector methods to find numerical solutions of the considered problems. The proposed scheme is based on discretizing the considered problems with respect to spatial and temporal domains. Numerical results are derived for some illustrative problems, and the outputs are compared with the exact solution in the integer order case. The solution behavior and 3D graphics of the discussed problems are demonstrated using the proposed scheme. Finally, the proposed scheme, which does not require solving large systems of linear equations, can be extended and modified to handle other classes of time-fractional PDEs. |
| Author | Odibat, Zaid |
| Author_xml | – sequence: 1 givenname: Zaid orcidid: 0000-0002-2414-7969 surname: Odibat fullname: Odibat, Zaid email: odibat@bau.edu.jo, z.odibat@gmail.com organization: Department of Mathematics, Faculty of Science, Al-Balqa Applied University, Salt 19117, Jordan |
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| Keywords | Fractional differential equation Initial-boundary value problem Predictor-corrector method Klein-Gordon equation Caputo derivative Finite difference method |
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| SubjectTerms | Caputo derivative Finite difference method Fractional differential equation Initial-boundary value problem Klein-Gordon equation Predictor-corrector method |
| Title | Numerical simulation for an initial-boundary value problem of time-fractional Klein-Gordon equations |
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