Analysis of Spectral Hamiltonian Boundary Value Methods (SHBVMs) for the numerical solution of ODE problems
Numerical Analysis
2025-01-20 v1
Abstract
Recently, the numerical solution of stiffly/highly-oscillatory Hamiltonian problems has been attacked by using Hamiltonian Boundary Value Methods (HBVMs) as spectral methods in time. While a theoretical analysis of this spectral approach has been only partially addressed, there is enough numerical evidence that it turns out to be very effective even when applied to a wider range of problems. Here we fill this gap by providing a thorough convergence analysis of the methods and confirm the theoretical results with the aid of a few numerical tests.
Keywords
Cite
@article{arxiv.1811.06800,
title = {Analysis of Spectral Hamiltonian Boundary Value Methods (SHBVMs) for the numerical solution of ODE problems},
author = {Pierluigi Amodio and Luigi Brugnano and Felice Iavernaro},
journal= {arXiv preprint arXiv:1811.06800},
year = {2025}
}
Comments
18 pages, 1 figure