Iterative methods for solving fractional differential equations using non-polynomial splines
In this work, a non-polynomial spline function is proposed to solve a linear fractional differential equation where the derivatives are in the Caputo sense. This approach transforms the fractional differential equation into a system of linear equations. The Gauss-Seidel and conjugate gradient method...
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| Format: | Article |
| Language: | English |
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EJAAM
2024-12-01
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| Series: | E-Journal of Analysis and Applied Mathematics |
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| Online Access: | https://ejaam.org/articles/2024/10.62780-ejaam-2024-003.pdf |
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| author | Faraidun K. Hamasalh Gulnar W. Sadiq Emad S. Salam |
| author_facet | Faraidun K. Hamasalh Gulnar W. Sadiq Emad S. Salam |
| author_sort | Faraidun K. Hamasalh |
| collection | DOAJ |
| description | In this work, a non-polynomial spline function is proposed to solve a linear fractional differential equation where the derivatives are in the Caputo sense. This approach transforms the fractional differential equation into a system of linear equations. The Gauss-Seidel and conjugate gradient methods are used to iteratively solve the linear system. Finally, to validate the method’s accuracy, several numerical examples with known analytical solutions are tested. According to the numerical experiments, the findings are in satisfactory agreement with the exact solutions. |
| format | Article |
| id | doaj-art-be2f8de7921840e9809d45656dfa1071 |
| institution | Kabale University |
| issn | 2544-9990 |
| language | English |
| publishDate | 2024-12-01 |
| publisher | EJAAM |
| record_format | Article |
| series | E-Journal of Analysis and Applied Mathematics |
| spelling | doaj-art-be2f8de7921840e9809d45656dfa10712025-02-08T18:35:22ZengEJAAME-Journal of Analysis and Applied Mathematics2544-99902024-12-01202410.62780/ejaam/2024-003Iterative methods for solving fractional differential equations using non-polynomial splinesFaraidun K. Hamasalh0Gulnar W. Sadiq1Emad S. Salam2Bakrajo Technical Institute, Sulaimani Polytechnic University, Sulaymaniyah, IraqDepartment of Mathematics, College of Basic Education, University of Sulaimani, Sulaymaniyah, IraqUniversity of Sulaimani, Sulaymaniyah, IraqIn this work, a non-polynomial spline function is proposed to solve a linear fractional differential equation where the derivatives are in the Caputo sense. This approach transforms the fractional differential equation into a system of linear equations. The Gauss-Seidel and conjugate gradient methods are used to iteratively solve the linear system. Finally, to validate the method’s accuracy, several numerical examples with known analytical solutions are tested. According to the numerical experiments, the findings are in satisfactory agreement with the exact solutions.https://ejaam.org/articles/2024/10.62780-ejaam-2024-003.pdffractional differential equationnon-polynomial splineconjugate gradient |
| spellingShingle | Faraidun K. Hamasalh Gulnar W. Sadiq Emad S. Salam Iterative methods for solving fractional differential equations using non-polynomial splines E-Journal of Analysis and Applied Mathematics fractional differential equation non-polynomial spline conjugate gradient |
| title | Iterative methods for solving fractional differential equations using non-polynomial splines |
| title_full | Iterative methods for solving fractional differential equations using non-polynomial splines |
| title_fullStr | Iterative methods for solving fractional differential equations using non-polynomial splines |
| title_full_unstemmed | Iterative methods for solving fractional differential equations using non-polynomial splines |
| title_short | Iterative methods for solving fractional differential equations using non-polynomial splines |
| title_sort | iterative methods for solving fractional differential equations using non polynomial splines |
| topic | fractional differential equation non-polynomial spline conjugate gradient |
| url | https://ejaam.org/articles/2024/10.62780-ejaam-2024-003.pdf |
| work_keys_str_mv | AT faraidunkhamasalh iterativemethodsforsolvingfractionaldifferentialequationsusingnonpolynomialsplines AT gulnarwsadiq iterativemethodsforsolvingfractionaldifferentialequationsusingnonpolynomialsplines AT emadssalam iterativemethodsforsolvingfractionaldifferentialequationsusingnonpolynomialsplines |