Speaker: Luigi Brugnano, Dipartimento di Matematica e Informatica “U.Dini”, University of Florence, Italy

Time : 15:00 - 16:00 CEST (Rome/Paris)

Hosted at: SISSA, International School of Advanced Studies, Trieste, Italy

Zoom : A Zoom link will appear here, an hour before the talk

Organizers : Pavan Pranjivan Mehta* (pavan.mehta@sissa.it) and Arran Fernandez** (arran.fernandez@emu.edu.tr)

* SISSA, International School of Advanced Studies, Italy

** Eastern Mediterranean University, Northern Cyprus

Keywords: FDEs, Caputo derivative, Fractional HBVMs, FHBVMs, Matlab^© software

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 [1, 4]. By suitably choosing the time-steps, such methods can achieve an arbitrarily high-order. As a matter of fact, corresponding Matlab^© codes have been made available on the web [2, 3, 4, 7] and a systematic comparison proved that such codes are extremely competitive with existing ones [5, 8]. This is still true when considering multi-order extensions of the methods [6]. In this talk, the main facts about FHBVMs will be recalled, showing that, in the case of an integer derivative, they reduce to “Hamiltonian Boundary Value Methods (HBVMs)”, a class of energy-conserving Runge-Kutta methods for the efficient numerical solution of Hamiltonian problems [9].

Biography: Luigi Brugnano is full professor on Numerical Analysis at the University of Florence, Italy. His research interests have concerned different fields of Applied and Numerical Mathematics, including: Numerical Linear Algebra, Mathematical Modelling, Numerical Methods for Differential Equations. He is author of over 160 scientific publications, and two research monographs. He is Co-Editor in Chief of the Journal of Computational and Applied Mathematics (Elsevier), and associated editor of several Journals in the field of Numerical Analysis and Applied Mathematics.

Bibliography

[1] L. Brugnano, K. Burrage, P. Burrage, F. Iavernaro. “A Spectrally Accurate Step-by-Step Method for the Numerical Solution of Fractional Differential Equations.” J. Sci. Comput. 99 (2024) art. 48. https://doi.org/10.1007/s10915-024-02517-1
[2] L. Brugnano, G. Gurioli, F. Iavernaro. “Numerical solution of FDE-IVPs by using Fractional HBVMs: the fhbvm code.” Numer. Algorithms 99 (2025) pp. 463-489. https://doi.org/10.1007/s11075-024-01884-y
[3] L. Brugnano, G. Gurioli, F. Iavernaro. “Solving FDE-IVPs by using Fractional HB-VMs: some experiments with the fhbvm code.” Journal of Computational Methods in Science and Engineering 25, 1 (2025) pp. 1030-1038. https://doi.org/10.1177/14727978251321328

[4] L. Brugnano, G. Gurioli, F. Iavernaro, M. Vikerpuur. “Analysis and implementation of collocation methods for fractional differential equations.” J. Sci. Comput. 104 (2025) art. 92. https://doi.org/10.1007/s10915-025-03006-9
[5] L. Brugnano, G. Gurioli, F. Iavernaro, M. Vikerpuur. “FDE-Testset: comparing Matlab codes for solving fractional differential equations of Caputo type.” Fractal Fract. 9, 5 (2025) art. 312. https://doi.org/10.3390/fractalfract9050312
[6] L. Brugnano, G. Gurioli, F. Iavernaro, M. Vikerpuur. “A multi-order extension of Fractional HBVMs (FHBVMs).” J. Sci. Comput. 107 (2026) art. 94. https://doi.org/10.1007/s10915-026-03315-7
[7] Fractional HBVMs Matlab^© Software: https://people.dimai.unifi.it/brugnano/fhbvm/
[8] FDE-Testset: https://people.dimai.unifi.it/brugnano/FDEtestset/

[9] L. Brugnano, F. Iavernaro. Line Integral Methods for Conservative Problems. Chapman et al./CRC, Boca Raton, 2016. https://doi.org/10.1201/b19319