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On solution of a class of nonlinear variable order fractional reaction–diffusion equation with Mittag–Leffler kernel
Author(s) -
Pandey Prashant,
GómezAguilar José Francisco
Publication year - 2021
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.22563
Subject(s) - mathematics , kernel (algebra) , chebyshev polynomials , chebyshev equation , chebyshev filter , nonlinear system , variable (mathematics) , convergence (economics) , mathematical analysis , algebraic equation , orthogonal polynomials , classical orthogonal polynomials , pure mathematics , physics , quantum mechanics , economics , economic growth
In this article, an efficient variable‐order Chebyshev collocation method which is based on shifted fifth‐kind Chebyshev polynomials is applied to solve a nonlinear variable‐order fractional reaction–diffusion equation with Mittag–Leffler kernel. The operational matrix of shifted fifth‐kind Chebyshev polynomials is derived for variable‐order ABC derivatives. The Chebyshev operational matrix together with the collocation method are applied to concerned nonlinear physical model with Mittag–Leffler kernel which is converted into a system of nonlinear algebraic equations, this system can be solved by using Newton method. The main focus of this paper is finding the convergence analysis of the approximation and high convergence order for small grid approximation. Few test examples with a comparison of maximum absolute error between the obtained numerical solution and existing known solution are being reported to show the accuracy and stability of the scheme. The physical presentation of the absolute errors for considered nonlinear variable‐order reaction–diffusion equations involving the Mittag–Leffler kernel with their exact solutions shows that the method is good for finding the solution of these kind of problems.