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arXiv · 2503.17719

Analysis and implementation of collocation methods for fractional differential equations

Luigi Brugnano·Gianmarco Gurioli·Felice Iavernaro·Mikk Vikerpuur
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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.

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Luigi Brugnano, Gianmarco Gurioli, Felice Iavernaro, Mikk Vikerpuur. 2025-03-22. Analysis and implementation of collocation methods for fractional differential equations. https://doi.org/10.1007/s10915-025-03006-9

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