A spectrally accurate step-by-step method for the numerical solution of 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.

26 pages, 2 figures, 7 tables, a few typos fixed in the updated version

References in corpus (4)

• Trapezoidal methods for fractional differential equations: theoretical and computational aspects
• Fractional diffusion equations and processes with randomly varying time
• (Spectral) Chebyshev collocation methods for solving differential equations
• A note on a stable algorithm for computing the fractional integrals of orthogonal polynomials

Cited by in corpus (4)

• Numerical solution of FDE-IVPs by using Fractional HBVMs: the fhbvm code
• Solving FDE-IVPs by using Fractional HBVMs: some experiments with the fhbvm code
• Analysis and implementation of collocation methods for fractional differential equations
• A shooting-Newton procedure for solving fractional terminal value problems