Numerical Integration Schemes for Finite Difference Solution of Time-Fractional Diffusion Equation with Generalized Caputo Derivative

Abstract

The algorithms of numerical computation of integrals that arise during the discretization of time-fractional diffusion equation with a generalized Caputo derivative are considered in the paper. We propose several algorithms based on the expansion of the integrand in the Taylor series which allow accelerating the computation of integrals in comparison with the recursive subdivision scheme. The results of the proposed algorithms performance testing are presented.