A note on the efficient implementation of Hamiltonian BVMs

TL;DR

This paper explores efficient implementation strategies for Hamiltonian BVMs, focusing on their blended formulation and exploiting problem structure for separable systems to enhance computational efficiency.

Contribution

It introduces an efficient implementation approach for Hamiltonian BVMs using blended formulation and leverages problem separability for improved performance.

Findings

Blended formulation enhances the efficiency of Hamiltonian BVMs.

Exploiting problem separability reduces computational cost.

The proposed methods improve energy preservation in simulations.

Abstract

We discuss the efficient implementation of Hamiltonian BVMs (HBVMs), a recently introduced class of energy preserving methods for canonical Hamiltonian systems, via their blended formulation. We also discuss the case of separable problems, for which the structure of the problem can be exploited to gain efficiency.