Development of the reproducing kernel Hilbert space algorithm for numerical pointwise solution of the time-fractional nonlocal reaction-diffusion equation

Autor: Omar Abu Arqub, Mohamed S. Osman, Choonkil Park, Jung Rye Lee, Hamed Alsulami, Mohammed Alhodaly
Jazyk: angličtina
Rok vydání: 2022
Předmět:
Zdroj: Alexandria Engineering Journal, Vol 61, Iss 12, Pp 10539-10550 (2022)
Druh dokumentu: article
ISSN: 1110-0168
DOI: 10.1016/j.aej.2022.04.008
Popis: It is notable that, the nonlocal reaction-diffusion equation carries math and computational physics to the core of extremely dynamic multidisciplinary studies that emerge from a huge assortment of uses. In this investigation, a totally new methodology for building a locally numerical pointwise solution is given by the agent the reproducing kernel algorithm. This is done utilizing a couple of generalized Hilpert spaces and their corresponding Green functions. The proposed calculation algorithm is applied to certain scalar issues problems to figure the arrangement solutions with Dirichlet constraints. By applying the procedures of the Gram–Schmidt process, orthonormalizing the basis, and truncating the optimized series, the approximate solutions are drawn, tabulated, and sketched. Introduced mathematical outcomes not only show the hidden superiority of the algorithm but also show its accurate efficiency. Finally, focused notes and futures planning works are mentioned with the most-used references.
Databáze: Directory of Open Access Journals