On the solution of hyperbolic two-dimensional fractional systems via discrete variational schemes of high order of accuracy
Электронный научный архив УРФУ
Информация об архиве | Просмотр оригинала| Поле | Значение | |
| Заглавие |
On the solution of hyperbolic two-dimensional fractional systems via discrete variational schemes of high order of accuracy
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| Автор |
Hendy, A. S.
Macías-Díaz, J. E. Serna-Reyes, A. J. |
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| Тематика |
DISCRETE VARIATIONAL METHOD
DISSIPATIVE TWO-DIMENSIONAL FRACTIONAL WAVE EQUATION STABILITY AND CONVERGENCE ANALYSES WEYL SPACE-FRACTIONAL OPERATORS WAVE EQUATIONS DAMPED WAVE EQUATIONS DISCRETE VARIATIONAL METHOD FRACTIONAL DERIVATIVES FRACTIONAL OPERATORS FRACTIONAL WAVE EQUATION HIGH ORDER COMPACT DIFFERENCE SCHEMES STABILITY AND CONVERGENCE VARIATIONAL STRUCTURES NUMERICAL METHODS |
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| Описание |
In this work, we consider a general class of damped wave equations in two spatial dimensions. The model considers the presence of Weyl space-fractional derivatives as well as a generic nonlinear potential. The system has an associated positive energy functional when damping is not present, in which case, the model is capable of preserving the energy throughout time. Meanwhile, the energy of the system is dissipated in the damped scenario. In this work, the Weyl space-fractional derivatives are approximated through second-order accurate fractional centered differences. A high-order compact difference scheme with fourth order accuracy in space and second order in time is proposed. Some associated discrete quantities are introduced to estimate the energy functional. We prove that the numerical method is capable of conserving the discrete variational structure under the same conditions for which the continuous model is conservative. The positivity of the discrete energy of the system is also discussed. The properties of consistency, solvability, stability and convergence of the proposed method are rigorously proved. We provide some numerical simulations that illustrate the agreement between the physical properties of the continuous and the discrete models. © 2018 Elsevier B.V.
Consejo Nacional de Ciencia y Tecnología, CONACYT; Government Council on Grants, Russian Federation For the first author, this work was supported by Government of the Russian Federation Resolution of March 16, 2013. RF Government Resolution of March 16, 2013. Meanwhile, the third author wishes to acknowledge the National Council of Science and Technology of Mexico (CONACYT) for partial financial support. Finally, the authors wish to thank the anonymous reviewers and the associate editor in charge of handling this manuscript for all their invaluable comments. Their criticisms and suggestions helped in improving the quality of this work. For the first author, this work was supported by Government of the Russian Federation Resolution 211 of March 16, 2013. RF Government Resolution 211 of March 16, 2013. Meanwhile, the third author wishes to acknowledge the National Council of Science and Technology of Mexico (CONACYT) for partial financial support. Finally, the authors wish to thank the anonymous reviewers and the associate editor in charge of handling this manuscript for all their invaluable comments. Their criticisms and suggestions helped in improving the quality of this work. |
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| Дата |
2024-04-23T11:10:50Z
2024-04-23T11:10:50Z 2019 |
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| Тип |
Article
Journal article (info:eu-repo/semantics/article) Published version (info:eu-repo/semantics/publishedVersion) |
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| Идентификатор |
Hendy, A. S., Macías-Díaz, J. E., & Serna-Reyes, A. J. (2019). On the solution of hyperbolic two-dimensional fractional systems via discrete variational schemes of high order of accuracy. Journal of Computational and Applied Mathematics, 354, 612–622. doi:10.1016/j.cam.2018.10.059
0377-0427 Final All Open Access, Bronze https://doi.org/10.1016/j.cam.2018.10.059 http://elar.urfu.ru/handle/10995/132544 10.1016/j.cam.2018.10.059 85058530696 000463300000052 |
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| Язык |
en
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| Права |
Open access (info:eu-repo/semantics/openAccess)
publisher-specific-oa |
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| Формат |
application/pdf
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| Издатель |
Elsevier B.V.
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| Источник |
Journal of Computational and Applied Mathematics
Journal of Computational and Applied Mathematics |
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