A two-grid temporal second-order scheme for the two-dimensional nonlinear Volterra integro-differential equation with weakly singular kernel
Электронный научный архив УРФУ
Информация об архиве | Просмотр оригинала| Поле | Значение | |
| Заглавие |
A two-grid temporal second-order scheme for the two-dimensional nonlinear Volterra integro-differential equation with weakly singular kernel
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| Автор |
Chen, H.
Qiu, W. Zaky, M. A. Hendy, A. S. |
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| Тематика |
ACCURATE SECOND ORDER
NONLINEAR FRACTIONAL EVOLUTION EQUATION NUMERICAL EXPERIMENTS STABILITY AND CONVERGENCE TIME TWO-GRID ALGORITHM APPROXIMATION ALGORITHMS INTEGRODIFFERENTIAL EQUATIONS ITERATIVE METHODS ACCURATE SECOND ORDER FRACTIONAL EVOLUTION EQUATIONS NONLINEAR FRACTIONAL EVOLUTION EQUATION NUMERICAL EXPERIMENTS SECOND ORDERS SECOND-ORDER SCHEME STABILITY AND CONVERGENCE TIME TWO-GRID ALGORITHM TWO-DIMENSIONAL TWO-GRID ALGORITHM NONLINEAR EQUATIONS |
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| Описание |
A two-grid temporal second-order scheme for the two-dimensional nonlinear Volterra integro-differential equation with a weakly singular kernel is of concern in this paper. The scheme is targeted to reduce the computation time and to improve the accuracy of the scheme developed by Xu et al. (Appl Numer Math 152:169–184, 2020). The constructed scheme is armed by three steps: First, a small nonlinear system is solved on the coarse grid using a fix-point iteration. Second, Lagrange’s linear interpolation formula is used to arrive at some auxiliary values for the analysis of the fine grid. Finally, a linearized Crank–Nicolson finite difference system is solved on the fine grid. Moreover, the algorithm uses a central difference approximation for the spatial derivatives. In the time direction, the time derivative and integral term are approximated by the Crank–Nicolson technique and product integral rule, respectively. By means of the discrete energy method, stability and space-time second-order convergence of the proposed approach are obtained in L2-norm. Finally, the numerical verification is fulfilled as the numerical results of the given numerical experiments agree with the theoretical analysis and verify the effectiveness of the algorithm. © 2023, The Author(s) under exclusive licence to Istituto di Informatica e Telematica (IIT).
CX20220454; Russian Science Foundation, RSF: 22-21-00075 The authors are grateful for helpful comments and suggestions from the reviewers. This work was supported by Postgraduate Scientific Research Innovation Project of Hunan Province (No. CX20220454). Ahmed S. Hendy wishes to acknowledge the support of the RSF grant, project 22-21-00075. |
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| Дата |
2024-04-05T16:38:45Z
2024-04-05T16:38:45Z 2023 |
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| Тип |
Article
Journal article (info:eu-repo/semantics/article) |info:eu-repo/semantics/submittedVersion |
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| Идентификатор |
Chen, H, Qiu, W, Zaky, MA & Hendy, AS 2023, 'A two-grid temporal second-order scheme for the two-dimensional nonlinear Volterra integro-differential equation with weakly singular kernel', Calcolo, Том. 60, № 1, 13. https://doi.org/10.1007/s10092-023-00508-6
Chen, H., Qiu, W., Zaky, M. A., & Hendy, A. S. (2023). A two-grid temporal second-order scheme for the two-dimensional nonlinear Volterra integro-differential equation with weakly singular kernel. Calcolo, 60(1), [13]. https://doi.org/10.1007/s10092-023-00508-6 0008-0624 Final All Open Access, Green https://www.scopus.com/inward/record.uri?eid=2-s2.0-85146944347&doi=10.1007%2fs10092-023-00508-6&partnerID=40&md5=3eaecbe41a7c8e98674f75ce84e566ff https://arxiv.org/pdf/2209.00211 http://elar.urfu.ru/handle/10995/131092 10.1007/s10092-023-00508-6 85146944347 000923278400001 |
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| Язык |
en
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| Связанные ресурсы |
info:eu-repo/grantAgreement/RSF//22-21-00075
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| Права |
Open access (info:eu-repo/semantics/openAccess)
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| Формат |
application/pdf
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| Издатель |
Springer International Publishing
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| Источник |
Calcolo
Calcolo |
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