The Hamiltonian BVMs (HBVMs) Homepage

2010/02/14 by Luigi Brugnano, Brugnano, Luigi, Felice Iavernaro +3
Engineering · Mathematics · #65H10 #65L05 #65L06 #65L80 #65P10 #Advanced Numerical Methods in Computational Mathematics #FOS: Mathematics #Numerical Analysis (math.NA) #Numerical methods for differential equations #Superconducting Materials and Applications

paper · pdf · doi:10.48550/arxiv.1002.2757

openalex publication_date 2010/02/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01

Abstract

Hamiltonian Boundary Value Methods (in short, HBVMs) is a new class of numerical methods for the efficient numerical solution of canonical Hamiltonian systems. In particular, their main feature is that of exactly preserving, for the numerical solution, the value of the Hamiltonian function, when the latter is a polynomial of arbitrarily high degree. Clearly, this fact implies a practical conservation of any analytical Hamiltonian function. In this notes, we collect the introductory material on HBVMs contained in the HBVMs Homepage, available at http://web.math.unifi.it/users/brugnano/HBVM/index.html

Citations

• Isospectral Property of Hamiltonian Boundary Value Methods (HBVMs) and their connections with Runge-Kutta collocation methods

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