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An efficient numerical approach to solve a class of variable‐order fractional integro‐partial differential equations
Author(s) -
Babaei Afshin,
Banihashemi Seddigheh,
Cattani Carlo
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.22546
Subject(s) - mathematics , discretization , sinc function , partial differential equation , variable (mathematics) , collocation method , kernel (algebra) , boundary value problem , convergence (economics) , mathematical analysis , transformation (genetics) , collocation (remote sensing) , differential equation , ordinary differential equation , biochemistry , chemistry , remote sensing , combinatorics , geology , economic growth , economics , gene
The main purpose of this work is to investigate an initial boundary value problem related to a suitable class of variable order fractional integro‐partial differential equations with a weakly singular kernel. To discretize the problem in the time direction, a finite difference method will be used. Then, the Sinc‐collocation approach combined with the double exponential transformation is employed to solve the problem in each time level. The proposed numerical algorithm is completely described and the convergence analysis of the numerical solution is presented. Finally, some illustrative examples are given to demonstrate the pertinent features of the proposed algorithm.