On the Rothe-Galerkin spectral discretization for a class of variable fractional-order nonlinear wave equations
Электронный научный архив УРФУ
Информация об архиве | Просмотр оригинала| Поле | Значение | |
| Заглавие |
On the Rothe-Galerkin spectral discretization for a class of variable fractional-order nonlinear wave equations
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| Автор |
Van, Bockstal, K.
Zaky, M. A. Hendy, A. |
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| Тематика |
EXISTENCE AND UNIQUENESS
FRACTIONAL CALCULUS GALERKIN SPECTRAL METHOD ROTHE’S DISCRETIZATION VARIABLE-ORDER WAVE EQUATION |
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| Описание |
In this contribution, a wave equation with a time-dependent variable-order fractional damping term and a nonlinear source is considered. Avoiding the circumstances of expressing the nonlinear variable-order fractional wave equations via closed-form expressions in terms of special functions, we investigate the existence and uniqueness of this problem with Rothe’s method. First, the weak formulation for the considered wave problem is proposed. Then, the uniqueness of a solution is established by employing Grönwall’s lemma. The Rothe scheme’s basic idea is to use Rothe functions to extend the solutions on single-time steps over the entire time frame. Inspired by that, we next introduce a uniform mesh time-discrete scheme based on a discrete convolution approximation in the backward sense. By applying some reasonable assumptions to the given data, we can predict a priori estimates for the time-discrete solution. Employing these estimates side by side with Rothe functions leads to proof of the solution’s existence over the whole time interval. Finally, the full discretisation of the problem is introduced by invoking Galerkin spectral techniques in the spatial direction, and numerical examples are given. © 2023, Diogenes Co.Ltd.
Russian Science Foundation, RSF: 22-21-00075; Bijzonder Onderzoeksfonds UGent, BOF: 01M01021 The work of K. Van Bockstal was supported by the Methusalem program of Ghent University Special Research Fund (BOF) (Grant Number 01M01021). A. S. Hendy wishes to acknowledge the support of the RSF, Russia grant, Project 22-21-00075. |
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| Дата |
2024-04-05T16:27:25Z
2024-04-05T16:27:25Z 2023 |
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| Тип |
Article
Journal article (info:eu-repo/semantics/article) |info:eu-repo/semantics/submittedVersion |
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| Идентификатор |
Van Bockstal, K, Zaky, M & Hendy, A 2023, 'On the Rothe-Galerkin spectral discretization for a class of variable fractional-order nonlinear wave equations', Fractional Calculus and Applied Analysis, Том. 26, № 5, стр. 2175-2201. https://doi.org/10.1007/s13540-023-00184-x
Van Bockstal, K., Zaky, M., & Hendy, A. (2023). On the Rothe-Galerkin spectral discretization for a class of variable fractional-order nonlinear wave equations. Fractional Calculus and Applied Analysis, 26(5), 2175-2201. https://doi.org/10.1007/s13540-023-00184-x 1311-0454 Final All Open Access, Green https://www.scopus.com/inward/record.uri?eid=2-s2.0-85164143059&doi=10.1007%2fs13540-023-00184-x&partnerID=40&md5=145847f550375795a8ed72e4069039fa https://arxiv.org/pdf/2303.03708 http://elar.urfu.ru/handle/10995/130617 10.1007/s13540-023-00184-x 85164143059 |
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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 Nature
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| Источник |
Fractional Calculus and Applied Analysis
Fractional Calculus and Applied Analysis |
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