Analysis and implementation of collocation methods for fractional differential equations

Abstract

Recently, the class of Runge-Kutta type methods named Fractional HBVMs (FHBVMs) has been introduced for the numerical solution of initial value problems of fractional differential equations, and a corresponding Matlab software has been released. Though an error analysis has already been given, a corresponding linear stability analysis is still lacking. We here provide such an analysis, together with some improvements concerning the mesh selection. This latter has been implemented into a new version of the code, which is available on the web.

30 pages, 10figures, 1 table

References in corpus (7)

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