A spectrally accurate step-by-step method for the numerical solution of fractional differential equations

TL;DR

This paper introduces a spectral accuracy numerical method for solving fractional differential equations using a step-by-step graded mesh and Jacobi polynomial expansion, validated by numerical examples.

Contribution

The paper presents a novel step-by-step graded mesh method employing Jacobi polynomial expansion for fractional differential equations, achieving spectral accuracy.

Findings

Method attains spectral accuracy under mild conditions

Numerical examples confirm theoretical predictions

Approach effectively solves fractional differential equations

Abstract

In this paper we consider the numerical solution of fractional differential equations. In particular, we study a step-by-step graded mesh procedure based on an expansion of the vector field using orthonormal Jacobi polynomials. Under mild hypotheses, the proposed procedure is capable of getting spectral accuracy. A few numerical examples are reported to confirm the theoretical findings.