Numerical integrators for motion under a strong constraining force
For computational scientists simulating systems with highly oscillatory dynamics, this provides accurate integration without step-size restrictions from stiffness.
This paper develops variants of the impulse method with projection for Hamiltonian systems with stiff anharmonic potentials, preserving adiabatic invariants and allowing macro-step sizes unrestricted by stiffness.
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.