An Efficient Explicit Decoupled Group Method for Solving Two–Dimensional Fractional Burgers’ Equation and Its Convergence Analysis
In this paper, the Crank–Nicolson (CN) and rotated four-point fractional explicit decoupled group (EDG) methods are introduced to solve the two-dimensional time–fractional Burgers’ equation. The EDG method is derived by the Taylor expansion and 45° rotation of the Crank–Nicolson method around the x...
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| Main Authors: | , , , , |
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| Format: | Article |
| Language: | English |
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Wiley
2021-01-01
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| Series: | Advances in Mathematical Physics |
| Online Access: | http://dx.doi.org/10.1155/2021/6669287 |
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| author | N. Abdi H. Aminikhah A. H. Refahi Sheikhani J. Alavi M. Taghipour |
| author_facet | N. Abdi H. Aminikhah A. H. Refahi Sheikhani J. Alavi M. Taghipour |
| author_sort | N. Abdi |
| collection | DOAJ |
| description | In this paper, the Crank–Nicolson (CN) and rotated four-point fractional explicit decoupled group (EDG) methods are introduced to solve the two-dimensional time–fractional Burgers’ equation. The EDG method is derived by the Taylor expansion and 45° rotation of the Crank–Nicolson method around the x and y axes. The local truncation error of CN and EDG is presented. Also, the stability and convergence of the proposed methods are proved. Some numerical experiments are performed to show the efficiency of the presented methods in terms of accuracy and CPU time. |
| format | Article |
| id | doaj-art-7ded8221546d4b889054b56ae8c8982a |
| institution | Kabale University |
| issn | 1687-9120 1687-9139 |
| language | English |
| publishDate | 2021-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Advances in Mathematical Physics |
| spelling | doaj-art-7ded8221546d4b889054b56ae8c8982a2025-02-03T06:43:48ZengWileyAdvances in Mathematical Physics1687-91201687-91392021-01-01202110.1155/2021/66692876669287An Efficient Explicit Decoupled Group Method for Solving Two–Dimensional Fractional Burgers’ Equation and Its Convergence AnalysisN. Abdi0H. Aminikhah1A. H. Refahi Sheikhani2J. Alavi3M. Taghipour4Department of Applied Mathematics and Computer Science, Faculty of Mathematical Sciences, University of Guilan, P.O. Box 1914, Rasht 41938, IranDepartment of Applied Mathematics and Computer Science, Faculty of Mathematical Sciences, University of Guilan, P.O. Box 1914, Rasht 41938, IranDepartment of Applied Mathematics, Faculty of Mathematical Sciences, Lahijan Branch, Islamic Azad University, Lahijan, IranDepartment of Applied Mathematics and Computer Science, Faculty of Mathematical Sciences, University of Guilan, P.O. Box 1914, Rasht 41938, IranDepartment of Applied Mathematics and Computer Science, Faculty of Mathematical Sciences, University of Guilan, P.O. Box 1914, Rasht 41938, IranIn this paper, the Crank–Nicolson (CN) and rotated four-point fractional explicit decoupled group (EDG) methods are introduced to solve the two-dimensional time–fractional Burgers’ equation. The EDG method is derived by the Taylor expansion and 45° rotation of the Crank–Nicolson method around the x and y axes. The local truncation error of CN and EDG is presented. Also, the stability and convergence of the proposed methods are proved. Some numerical experiments are performed to show the efficiency of the presented methods in terms of accuracy and CPU time.http://dx.doi.org/10.1155/2021/6669287 |
| spellingShingle | N. Abdi H. Aminikhah A. H. Refahi Sheikhani J. Alavi M. Taghipour An Efficient Explicit Decoupled Group Method for Solving Two–Dimensional Fractional Burgers’ Equation and Its Convergence Analysis Advances in Mathematical Physics |
| title | An Efficient Explicit Decoupled Group Method for Solving Two–Dimensional Fractional Burgers’ Equation and Its Convergence Analysis |
| title_full | An Efficient Explicit Decoupled Group Method for Solving Two–Dimensional Fractional Burgers’ Equation and Its Convergence Analysis |
| title_fullStr | An Efficient Explicit Decoupled Group Method for Solving Two–Dimensional Fractional Burgers’ Equation and Its Convergence Analysis |
| title_full_unstemmed | An Efficient Explicit Decoupled Group Method for Solving Two–Dimensional Fractional Burgers’ Equation and Its Convergence Analysis |
| title_short | An Efficient Explicit Decoupled Group Method for Solving Two–Dimensional Fractional Burgers’ Equation and Its Convergence Analysis |
| title_sort | efficient explicit decoupled group method for solving two dimensional fractional burgers equation and its convergence analysis |
| url | http://dx.doi.org/10.1155/2021/6669287 |
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