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http://elar.urfu.ru/handle/10995/90076
Название: | Discrete monotone method for space-fractional nonlinear reaction–diffusion equations |
Авторы: | Flores, S. Macías-Díaz, J. E. Hendy, A. S. |
Дата публикации: | 2019 |
Издатель: | Springer International Publishing |
Библиографическое описание: | Flores, S. Discrete monotone method for space-fractional nonlinear reaction–diffusion equations / S. Flores, J. E. Macías-Díaz, A. S. Hendy. — DOI 10.1186/s13662-019-2267-1 // Advances in Difference Equations. — 2019. — Vol. 1. — Iss. 2019. — 317. |
Аннотация: | A discrete monotone iterative method is reported here to solve a space-fractional nonlinear diffusion–reaction equation. More precisely, we propose a Crank–Nicolson discretization of a reaction–diffusion system with fractional spatial derivative of the Riesz type. The finite-difference scheme is based on the use of fractional-order centered differences, and it is solved using a monotone iterative technique. The existence and uniqueness of solutions of the numerical model are analyzed using this approach, along with the technique of upper and lower solutions. This methodology is employed also to prove the main numerical properties of the technique, namely, the consistency, stability, and convergence. As an application, the particular case of the space-fractional Fisher’s equation is theoretically analyzed in full detail. In that case, the monotone iterative method guarantees the preservation of the positivity and the boundedness of the numerical approximations. Various numerical examples are provided to illustrate the validity of the numerical approximations. More precisely, we provide an extensive series of comparisons against other numerical methods available in the literature, we show detailed numerical analyses of convergence in time and in space against fractional and integer-order models, and we provide studies on the robustness and the numerical performance of the discrete monotone method. © 2019, The Author(s). |
Ключевые слова: | CRANK–NICOLSON FINITE-DIFFERENCE SCHEME DISCRETE MONOTONE ITERATIVE METHOD EXISTENCE AND UNIQUENESS OF SOLUTIONS NUMERICAL EFFICIENCY ANALYSIS SPACE-FRACTIONAL DIFFUSION–REACTION EQUATIONS |
URI: | http://elar.urfu.ru/handle/10995/90076 |
Условия доступа: | info:eu-repo/semantics/openAccess cc-by |
Идентификатор SCOPUS: | 85070193052 |
Идентификатор WOS: | 000478914900001 |
Идентификатор PURE: | 10469438 |
ISSN: | 1687-1839 |
DOI: | 10.1186/s13662-019-2267-1 |
Сведения о поддержке: | Russian Foundation for Basic Research, RFBR: 19-01-00019 Consejo Nacional de Ciencia y TecnologÃa, CONACYT: A1-S-45928 The first author would like to acknowledge the financial support of the National Council for Science and Technology of Mexico (CONACYT). The second (and corresponding) author acknowledges financial support from CONACYT through grant A1-S-45928. ASH is financed by RFBR Grant 19-01-00019. |
Располагается в коллекциях: | Научные публикации ученых УрФУ, проиндексированные в SCOPUS и WoS CC |
Файлы этого ресурса:
Файл | Описание | Размер | Формат | |
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10.1186-s13662-019-2267-1.pdf | 3,28 MB | Adobe PDF | Просмотреть/Открыть |
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