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

arXiv comment28 pages, 4 figures (a few typos fixed)

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Cited by in corpus (15)

• Spectrally accurate space-time solution of Hamiltonian PDEs
• Arbitrarily high-order energy-preserving methods for simulating the gyrocenter dynamics of charged particles
• Analysis of Spectral Hamiltonian Boundary Value Methods (SHBVMs) for the numerical solution of ODE problems
• Line Integral solution of Hamiltonian PDEs
• A spectrally accurate step-by-step method for the numerical solution of fractional differential equations
• A note on the continuous-stage Runge-Kutta-(Nyström) formulation of Hamiltonian Boundary Value Methods (HBVMs)
• A new framework for polynomial approximation to differential equations
• Arbitrarily high-order energy-conserving methods for Poisson problems
• (Spectral) Chebyshev collocation methods for solving differential equations
• Simply improved averaging for coupled oscillators and weakly nonlinear waves
• Spectrally accurate space-time solution of Manakov systems
• Numerical solution of FDE-IVPs by using Fractional HBVMs: the fhbvm code
• Solving FDE-IVPs by using Fractional HBVMs: some experiments with the fhbvm code
• A shooting-Newton procedure for solving fractional terminal value problems
• Continuous-Stage Runge-Kutta approximation to Differential Problems