The Hamiltonian BVMs (HBVMs) Homepage

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

49 pages, 16 figures; Chapter 4 modified; minor corrections to Chapter 5; References updated

References in corpus (3)

• Hamiltonian Boundary Value Methods (Energy Conserving Discrete Line Integral Methods)
• Isospectral Property of Hamiltonian Boundary Value Methods (HBVMs) and their connections with Runge-Kutta collocation methods
• Blended General Linear Methods based on Boundary Value Methods in the GBDF family

Cited by in corpus (7)

• A unifying framework for the derivation and analysis of effective classes of one-step methods for ODEs
• On the Existence of Energy-Preserving Symplectic Integrators Based upon Gauss Collocation Formulae
• A note on the efficient implementation of Hamiltonian BVMs
• The Lack of Continuity and the Role of Infinite and Infinitesimal in Numerical Methods for ODEs: the Case of Symplecticity
• A Two Step, Fourth Order, Nearly-Linear Method with Energy Preserving Properties
• Isospectral Property of Hamiltonian Boundary Value Methods (HBVMs) and their connections with Runge-Kutta collocation methods
• LINE INTEGRAL METHODS and their application to the numerical solution of conservative problems