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A high order numerical scheme for solving a class of non‐homogeneous time‐fractional reaction diffusion equation
Author(s) -
Roul Pradip,
Goura V. M. K. Prasad
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.22594
Subject(s) - mathematics , fractional calculus , discretization , reaction–diffusion system , mathematical analysis , convergence (economics) , diffusion equation , collocation method , differential equation , ordinary differential equation , economy , economic growth , economics , service (business)
This paper is concerned with the development of a high order numerical technique for solving time‐fractional reaction–diffusion equation. The fractional derivative in the governing equation is described in the Caputo sense and a collocation method based on quintic B‐spline basis function is used to discretize the space variable. The stability and convergence analysis of the method are investigated, and it is shown that the proposed method converges to the exact solution of the problem with order of convergence O (Δ t 2 − α + Δ x 4 ) , where α is the order of fractional derivative (0 < α < 1) . Three test problems are considered to illustrate the efficiency and accuracy of present numerical scheme and to verify the theoretical result. It is shown that the order of fractional derivative has a profound effect on the solution of time‐fractional reaction–diffusion equation.