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A novel variable‐order fractional nonlinear Klein Gordon model: A numerical approach
Author(s) -
Sweilam Nasser H.,
AlMekhlafi Seham M.,
Albalawi Anan O.
Publication year - 2019
Publication title -
numerical methods for partial differential equations
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.901
H-Index - 61
eISSN - 1098-2426
pISSN - 0749-159X
DOI - 10.1002/num.22367
Subject(s) - mathematics , truncation error , nonlinear system , stability (learning theory) , convergence (economics) , variable (mathematics) , fractional calculus , truncation (statistics) , finite difference method , order (exchange) , rate of convergence , finite difference , mathematical analysis , statistics , channel (broadcasting) , physics , engineering , finance , quantum mechanics , machine learning , computer science , electrical engineering , economics , economic growth
In this article, a novel variable order fractional nonlinear Klein Gordon model is presented where the variable‐order fractional derivative is defined in the Caputo sense. The merit of nonstandard numerical techniques is extended here and we present the weighted average nonstandard finite difference method to study numerically the proposed model. Special attention is paid to study the convergence and to the stability analysis of the numerical technique. Moreover, the truncation error is analyzed. Three test examples are provided. Comparative studies are done between the used numerical technique and the weighted average finite difference method. It is found that the stability regions are larger by using the weighted average nonstandard finite difference method.