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

2015/03/10 by Dimitrov, Yuri
#FOS: Mathematics #Numerical Analysis (math.NA)

paper · doi:10.48550/arxiv.1503.02958

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.

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