High-order numerical algorithm for fractional-order nonlinear diffusion equations with a time delay effect
Электронный научный архив УРФУ
Информация об архиве | Просмотр оригинала| Поле | Значение | |
| Заглавие |
High-order numerical algorithm for fractional-order nonlinear diffusion equations with a time delay effect
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| Автор |
Omran, A. K.
Pimenov, V. G. |
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| Тематика |
ALIKHANOV L2 − 1Σ FORMULA
DISCRETE FRACTIONAL GRÖNWALL INEQUALITIES FRACTIONAL DIFFUSION EQUATIONS LEGENDRE-GALERKIN SPECTRAL METHOD TIME DELAY MATHEMATICS |
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| Описание |
In this paper, we examine and provide numerical solutions to the nonlinear fractional order time-space diffusion equations with the influence of temporal delay. An effective high-order numerical scheme that mixes the so-called Alikhanov L2 − 1σ formula side by side to the power of the Galerkin method is presented. Specifically, the time-fractional component is estimated using the uniform L2−1σ difference formula, while the spatial fractional operator is approximated using the Legendre-Galerkin spectral approximation. In addition, Taylor’s approximations are used to discretize the term of the nonlinear source function. It has been shown theoretically that the suggested scheme’s numerical solution is unconditionally stable, with a second-order time-convergence and a space-convergent order of exponential rate. Furthermore, a suitable discrete fractional Grönwall inequality is then utilized to quantify error estimates for the derived solution. Finally, we provide a numerical test that closely matches the theoretical investigation to assess the efficacy of the suggested method. © 2023 the Author(s), licensee AIMS Press.
Russian Science Foundation, RSF: 22-21-00075 The authors are grateful to the handling editor and the anonymous referees for their constructive feedback and helpful suggestions, which highly improved the paper. V.G. Pimenov wishes to acknowledge the support of the RSF grant, project 22-21-00075. |
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| Дата |
2024-04-05T16:27:42Z
2024-04-05T16:27:42Z 2023 |
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| Тип |
Article
Journal article (info:eu-repo/semantics/article) |info:eu-repo/semantics/publishedVersion |
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| Идентификатор |
Omran, AK & Pimenov, VG 2023, 'High-order numerical algorithm for fractional-order nonlinear diffusion equations with a time delay effect', Aims mathematics, Том. 8, № 4, стр. 7672-7694. https://doi.org/10.3934/math.2023385
Omran, A. K., & Pimenov, V. G. (2023). High-order numerical algorithm for fractional-order nonlinear diffusion equations with a time delay effect. Aims mathematics, 8(4), 7672-7694. https://doi.org/10.3934/math.2023385 2473-6988 Final All Open Access, Gold https://www.scopus.com/inward/record.uri?eid=2-s2.0-85146363287&doi=10.3934%2fmath.2023385&partnerID=40&md5=e25582240ce8b684e6b0ac25eee0d157 https://doi.org/10.3934/math.2023385 http://elar.urfu.ru/handle/10995/130637 10.3934/math.2023385 85146363287 000961960200006 |
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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)
cc-by https://creativecommons.org/licenses/by/4.0/ |
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| Формат |
application/pdf
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| Издатель |
American Institute of Mathematical Sciences
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| Источник |
AIMS Mathematics
AIMS Mathematics |
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