A fourth order non-polynomial quintic spline collocation technique for solving time fractional superdiffusion equations

Abstract

Abstract The purpose of this article is to present a technique for the numerical solution of Caputo time fractional superdiffusion equation. The central difference approximation is used to discretize the time derivative, while non-polynomial quintic spline is employed as an interpolating function in the spatial direction. The proposed method is shown to be unconditionally stable and O(h4+Δt2) $O(h^{4}+\Delta t^{2})$ accurate. In order to check the feasibility of the proposed technique, some test examples have been considered and the simulation results are compared with those available in the existing literature.

Keywords

• Non-polynomial quintic spline
• Finite central difference approach
• Superdiffusion equation
• Caputo time fractional derivative