AIMS Mathematics (Apr 2023)

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

  • Muhammad Asim Khan ,
  • Norma Alias ,
  • Umair Ali

DOI
https://doi.org/10.3934/math.2023697
Journal volume & issue
Vol. 8, no. 6
pp. 13725 – 13746

Abstract

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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.

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