A pseudo energy-invariant method for relativistic wave equations with Riesz space-fractional derivatives
Электронный научный архив УРФУ
Информация об архиве | Просмотр оригинала| Поле | Значение | |
| Заглавие |
A pseudo energy-invariant method for relativistic wave equations with Riesz space-fractional derivatives
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| Автор |
Macías-Díaz, J. E.
Hendy, A. S. De, Staelen, R. H. |
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| Тематика |
ENERGY-PRESERVING FINITE-DIFFERENCE SCHEME
NONLINEAR RELATIVISTIC WAVE EQUATION NONLINEAR SUPRATRANSMISSION RIESZ SPACE-FRACTIONAL DERIVATIVES FINITE DIFFERENCE METHOD ITERATIVE METHODS QUANTUM THEORY SINE-GORDON EQUATION COMPUTATIONAL COMPARISONS FINITE DIFFERENCE SCHEME FINITE-DIFFERENCE DISCRETIZATION FRACTIONAL DERIVATIVES NONLINEAR SUPRATRANSMISSION NONLINEAR WAVE EQUATION RELATIVISTIC QUANTUM MECHANICS RELATIVISTIC WAVE EQUATIONS NONLINEAR EQUATIONS |
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| Описание |
In this work, we investigate a general nonlinear wave equation with Riesz space-fractional derivatives that generalizes various classical hyperbolic models, including the sine-Gordon and the Klein–Gordon equations from relativistic quantum mechanics. A finite-difference discretization of the model is provided using fractional centered differences. The method is a technique that is capable of preserving an energy-like quantity at each iteration. Some computational comparisons against solutions available in the literature are performed in order to assess the capability of the method to preserve the invariant. Our experiments confirm that the technique yields good approximations to the solutions considered. As an application of our scheme, we provide simulations that confirm, for the first time in the literature, the presence of the phenomenon of nonlinear supratransmission in Riesz space-fractional Klein–Gordon equations driven by a harmonic perturbation at the boundary. © 2017 Elsevier B.V.
FWO15/PDO/076 The third author acknowledges the support of the Research Foundation—Flanders ( FWO15/PDO/076 ). Finally, the authors wish to thank the anonymous reviewers and the editor in charge of handling this paper for their suggestions and criticisms. Their comments helped in improving the quality of this manuscript. |
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| Дата |
2024-04-17T17:43:38Z
2024-04-17T17:43:38Z 2018 |
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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 |
Macias-Diaz, J. E., Hendy, A. S., & De Staelen, R. H. (2018). A pseudo energy-invariant method for relativistic wave equations with Riesz space-fractional derivatives. Computer Physics Communications, 224, 98-107. https://doi.org/10.1016/j.cpc.2017.11.008
0010-4655 Final All Open Access, Green https://biblio.ugent.be/publication/8549240/file/8652449 http://elar.urfu.ru/handle/10995/132197 10.1016/j.cpc.2017.11.008 85036615303 000424726700008 |
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| Язык |
en
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| Права |
Open access (info:eu-repo/semantics/openAccess)
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| Формат |
application/pdf
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| Издатель |
Elsevier B.V.
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| Источник |
Computer Physics Communications
Computer Physics Communications |
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