@article{Khan2023, 
author = {Muhammad Asim Khan and Norma Alias and Umair Ali},
title = {A new fourth-order grouping iterative method for the time fractional sub-diffusion equation having a weak singularity at initial time},
year = {2023},
journal = {AIMS Mathematics},
volume = {8},
number = {6},
pages = {13725-13746},
keywords = {sub-diffusion equation, Crank-Nicolson, grouping method, convergence and stability, fourth-order FDM, captive fractional discretisation},
url = {https://www.sciopen.com/article/10.3934/math.2023697},
doi = {10.3934/math.2023697},
abstract = {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.}
}