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

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.

Keywords

• sub-diffusion equation
• crank-nicolson
• grouping method
• convergence and stability
• fourth-order fdm
• captive fractional discretisation