Accuracy and speed of splitting methods for three-dimensional space–time fractional diffusion equation with [formula omitted]-Caputo derivatives

Abstract

The paper deals with finite-difference schemes for a three-dimensional diffusion equation with ψ-Caputo derivative with respect to the time and space variables. Theoretical and experimental estimates of accuracy and performance of implicit and splitting schemes are given. Finite-difference schemes are combined with algorithms that accelerate computations on the base of fixed memory principle and expansion of integral operator kernel into series. Computational experiments are conducted on a test problem that has an analytical solution for the case of the Caputo–Katugampola derivative. In the experiments we focus on the issue of interdependence between accuracy and speed of calculations. Based on the obtained estimates, we present an algorithm for automatic selection of optimal computational scheme.