A New Method for Numerical Solution of the Fractional Relaxation and Subdiffusion Equations Using Fractional Taylor Polynomials

Abstract

The accuracy of the numerical solution of a fractional differential equation depends on the differentiability class of the solution. The derivatives of the solutions of fractional differential equations often have a singularity at the initial point, which may result in a lower accuracy of the numerical solutions. We propose a method for improving the accuracy of the numerical solutions of the fractional relaxation and subdiffusion equations based on the fractional Taylor polynomials of the solution at the initial point.

References in corpus (3)

• An analysis of the L1 Scheme for the subdiffusion equation with nonsmooth data
• Two Schemes for Fractional Diffusion and Diffusion-Wave Equations with Nonsmooth Data
• A Second Order Approximation for the Caputo Fractional Derivative

Cited by in corpus (2)

• Three-Point Compact Approximation for the Caputo Fractional Derivative
• High order finite difference schemes on non-uniform meshes for the time-fractional Black-Scholes equation