High-order finite difference method based on linear barycentric rational interpolation for Caputo type sub-diffusion equation

Abstract

The main aim of this paper is to develop a class of high-order finite difference method for the numerical solution of Caputo type time-fractional sub-diffusion equation. In the time direction, the Caputo derivative is discretized by employing a numerical technique based on the fractional linear barycentric rational interpolation method (FLBRI). The stability properties and the convergence analysis of the proposed scheme are considered based on the energy method. As a result, the order of convergence is O(Δt)p+(Δx)2 for 1≤p≤7, in which Δt is the temporal step size, Δx is the spatial step size, and p is the order of accuracy in the time direction. Finally, numerical experiment is provided to show that the results confirm the theoretical analysis, perfectly.