Numerical integrators for motion under a strong constraining force

2014/03/17 by Christian Lubich, Lubich, Christian, Daniel J. Weiss +1
Mathematics · Physics and Astronomy · #FOS: Mathematics #Fractional Differential Equations Solutions #Model Reduction and Neural Networks #Numerical Analysis (math.NA) #Numerical methods for differential equations

paper · pdf · doi:10.48550/arxiv.1403.4274

openalex publication_date 2014/03/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01

Abstract

This paper deals with the numerical integration of Hamiltonian systems in which a stiff anharmonic potential causes highly oscillatory solution behavior with solution-dependent frequencies. The impulse method, which uses micro- and macro-steps for the integration of fast and slow parts, respectively, does not work satisfactorily on such problems. Here it is shown that variants of the impulse method with suitable projection preserve the actions as adiabatic invariants and yield accurate approximations, with macro-stepsizes that are not restricted by the stiffness parameter.

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