New preconditioning and half-sweep accelerated overrelaxation solution for fractional differential equation
The present paper investigates the approximate solution of a one-dimensional linear space-fractional diffusion equation using a new preconditioning matrix to develop an efficient half-sweep accelerated overrelaxation iterative method. The proposed method utilizes unconditionally stable implicit fini...
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| Format: | Article |
| Language: | English |
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Elsevier
2023-02-01
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| Series: | Journal of King Saud University: Science |
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| Online Access: | http://www.sciencedirect.com/science/article/pii/S1018364722006425 |
| _version_ | 1797952839732953088 |
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| author | Praveen Agarwal Andang Sunarto Jackel Vui Lung Chew Jumat Sulaiman Shaher Momani |
| author_facet | Praveen Agarwal Andang Sunarto Jackel Vui Lung Chew Jumat Sulaiman Shaher Momani |
| author_sort | Praveen Agarwal |
| collection | DOAJ |
| description | The present paper investigates the approximate solution of a one-dimensional linear space-fractional diffusion equation using a new preconditioning matrix to develop an efficient half-sweep accelerated overrelaxation iterative method. The proposed method utilizes unconditionally stable implicit finite difference schemes to formulate the discrete approximation equation to the problem. The formulation employs the Caputo fractional derivative to treat the space-fractional derivative in the problem. The paper's focus is to assess the improvement in terms of the convergence rate of the solution obtained by the proposed iterative method. The numerical experiment illustrates the superiority of the proposed method in terms of solution efficiency against one of the existing preconditioned methods, preconditioned accelerated overrelaxation and implicit Euler method. The proposed method reveals the ability to compute the solution with lesser iterations and faster computation time than the preconditioned accelerated overrelaxation and implicit Euler method. The method introduced in the paper, half-sweep preconditioned accelerated overrelaxation, has the potential to solve a variety of space-fractional diffusion models efficiently. Future investigation will improve the absolute errors of the solutions. |
| first_indexed | 2024-04-10T22:52:22Z |
| format | Article |
| id | doaj.art-3f4180c4d1e24b70a4db715dda4d2505 |
| institution | Directory Open Access Journal |
| issn | 1018-3647 |
| language | English |
| last_indexed | 2024-04-10T22:52:22Z |
| publishDate | 2023-02-01 |
| publisher | Elsevier |
| record_format | Article |
| series | Journal of King Saud University: Science |
| spelling | doaj.art-3f4180c4d1e24b70a4db715dda4d25052023-01-15T04:21:13ZengElsevierJournal of King Saud University: Science1018-36472023-02-01352102461New preconditioning and half-sweep accelerated overrelaxation solution for fractional differential equationPraveen Agarwal0Andang Sunarto1Jackel Vui Lung Chew2Jumat Sulaiman3Shaher Momani4Anand International College of Engineering, Agra Road, Jaipur, Rajasthan 303012, India; International Center for Basic and Applied Sciences, Jaipur 302029, India; Peoples' Friendship University of Russia (RUDN University), 6 Miklukho-Maklaya St, 117198 Moscow, Russian Federation; Nonlinear Dynamics Research Center (NDRC), Ajman University, Ajman, United Arab Emirates; Corresponding authors at: Anand International College of Engineering, Agra Road, Jaipur, Rajasthan 303012, India (P. Agarwal); Tadris Matematika, UIN Fatmawati Sukarno Bengkulu, Bengkulu 38211, Indonesia.Tadris Matematika, UIN Fatmawati Sukarno Bengkulu, Bengkulu 38211, Indonesia; Corresponding authors at: Anand International College of Engineering, Agra Road, Jaipur, Rajasthan 303012, India (P. Agarwal); Tadris Matematika, UIN Fatmawati Sukarno Bengkulu, Bengkulu 38211, Indonesia.Faculty of Computing and Informatics, Universiti Malaysia Sabah Labuan International Campus, Labuan F.T. 87000, MalaysiaFaculty of Science and Natural Resources, Universiti Malaysia Sabah, Kota Kinabalu, Sabah 88400, MalaysiaNonlinear Dynamics Research Center (NDRC), Ajman University, Ajman, United Arab Emirates; Department of Mathematics, Faculty of Science, University of Jordan, Amman 11942, Jordan (A. Sunarto).The present paper investigates the approximate solution of a one-dimensional linear space-fractional diffusion equation using a new preconditioning matrix to develop an efficient half-sweep accelerated overrelaxation iterative method. The proposed method utilizes unconditionally stable implicit finite difference schemes to formulate the discrete approximation equation to the problem. The formulation employs the Caputo fractional derivative to treat the space-fractional derivative in the problem. The paper's focus is to assess the improvement in terms of the convergence rate of the solution obtained by the proposed iterative method. The numerical experiment illustrates the superiority of the proposed method in terms of solution efficiency against one of the existing preconditioned methods, preconditioned accelerated overrelaxation and implicit Euler method. The proposed method reveals the ability to compute the solution with lesser iterations and faster computation time than the preconditioned accelerated overrelaxation and implicit Euler method. The method introduced in the paper, half-sweep preconditioned accelerated overrelaxation, has the potential to solve a variety of space-fractional diffusion models efficiently. Future investigation will improve the absolute errors of the solutions.http://www.sciencedirect.com/science/article/pii/S1018364722006425Finite difference methodCaputo fractional derivativeSpace-fractional derivativeHalf-sweepPreconditioning matrixAccelerated overrelaxation |
| spellingShingle | Praveen Agarwal Andang Sunarto Jackel Vui Lung Chew Jumat Sulaiman Shaher Momani New preconditioning and half-sweep accelerated overrelaxation solution for fractional differential equation Journal of King Saud University: Science Finite difference method Caputo fractional derivative Space-fractional derivative Half-sweep Preconditioning matrix Accelerated overrelaxation |
| title | New preconditioning and half-sweep accelerated overrelaxation solution for fractional differential equation |
| title_full | New preconditioning and half-sweep accelerated overrelaxation solution for fractional differential equation |
| title_fullStr | New preconditioning and half-sweep accelerated overrelaxation solution for fractional differential equation |
| title_full_unstemmed | New preconditioning and half-sweep accelerated overrelaxation solution for fractional differential equation |
| title_short | New preconditioning and half-sweep accelerated overrelaxation solution for fractional differential equation |
| title_sort | new preconditioning and half sweep accelerated overrelaxation solution for fractional differential equation |
| topic | Finite difference method Caputo fractional derivative Space-fractional derivative Half-sweep Preconditioning matrix Accelerated overrelaxation |
| url | http://www.sciencedirect.com/science/article/pii/S1018364722006425 |
| work_keys_str_mv | AT praveenagarwal newpreconditioningandhalfsweepacceleratedoverrelaxationsolutionforfractionaldifferentialequation AT andangsunarto newpreconditioningandhalfsweepacceleratedoverrelaxationsolutionforfractionaldifferentialequation AT jackelvuilungchew newpreconditioningandhalfsweepacceleratedoverrelaxationsolutionforfractionaldifferentialequation AT jumatsulaiman newpreconditioningandhalfsweepacceleratedoverrelaxationsolutionforfractionaldifferentialequation AT shahermomani newpreconditioningandhalfsweepacceleratedoverrelaxationsolutionforfractionaldifferentialequation |