A new fourth-order grouping iterative method for the time fractional sub-diffusion equation having a weak singularity at initial time-Reference-Cited by-同舟云学术

A new fourth-order grouping iterative method for the time fractional sub-diffusion equation having a weak singularity at initial time

Published:2023 Issue:6 Volume:8 Page:13725-13746
ISSN:2473-6988
Container-title:AIMS Mathematics
language:
Short-container-title:MATH

Author:

Khan Muhammad Asim¹,Alias Norma¹,Ali Umair²

Affiliation:

1. Department of Mathematical Sciences, Faculty of Science, Universiti Teknologi, Malaysia

2. Department of Applied Mathematics and Statistics, Institute of Space Technology, Pakistan

Abstract

<abstract><p>A new fourth-order explicit grouping iterative method is constructed for the numerical solution of the fractional sub-diffusion equation. The discretization of the equation is based on fourth-order finite difference method. Captive fractional discretization having functions with a weak singularity at $ t = 0 $ is used for time and similarly, the space derivative is approximated with the help of fourth-order approximation. Furthermore, the convergence and stability of the scheme are analyzed. Finally, the accuracy and validity are investigated by some numerical examples.</p></abstract>

Publisher

American Institute of Mathematical Sciences (AIMS)

Subject

General Mathematics

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