Solving FDE-IVPs by using Fractional HBVMs: some experiments with the fhbvm code

TL;DR

This paper presents numerical experiments demonstrating the effectiveness of Fractional HBVMs, implemented via an extended Matlab code, for solving initial value problems in fractional differential equations.

Contribution

It introduces and tests an extension of the fhbvm Matlab code implementing Fractional HBVMs for FDE-IVPs, showing their practical effectiveness.

Findings

Fractional HBVMs are effective for FDE-IVPs.

The extended fhbvm code successfully implements these methods.

Numerical experiments confirm the methods' accuracy and efficiency.

Abstract

In this paper we report a few numerical tests by using a slight extension of the Matlab code fhbvm in [8], implementing Fractional HBVMs, a recently introduced class of numerical methods for solving Initial Value Problems of Fractional Differential Equations (FDE-IVPs). The reported experiments are aimed to give evidence of its effectiveness.