On the effectiveness of spectral methods for the numerical solution of multi-frequency highly-oscillatory Hamiltonian problems

TL;DR

This paper introduces a variant of Hamiltonian Boundary Value Methods tailored for efficiently solving multi-frequency, highly-oscillatory Hamiltonian problems common in real-world applications.

Contribution

A novel variant of HBVMs designed specifically for the numerical solution of complex multi-frequency oscillatory Hamiltonian systems.

Findings

Efficiently handles multi-frequency oscillations.

Preserves Hamiltonian structure during numerical integration.

Applicable to real-world oscillatory problems.

Abstract

Multi-frequency, highly-oscillatory Hamiltonian problems derive from the mathematical modelling of many real life applications. We here propose a variant of Hamiltonian Boundary Value Methods (HBVMs), which is able to efficiently deal with the numerical solution of such problems.