S. Novo and J. Rojo

Numer. Math., 61 (1992), pp. 261-264

Abstract:

Kirchgraber derived in 1988 an integration procedure (called the LIPS-code) for long-term prediction of the solutions of equations which are perturbations of systems having only periodic solutions. His basic idea is to use the Poincaré map to define a new system which can be integrated with large step-size; the method is specially sucessful when the period is close to the unperturbed one. Obviously the size of the perturbation modifies the period and therefore affects the precision of the algorithm. In this paper we propose a double modification of Kirchgraber's code: to use a first-order approximation of the perturbed period instead of the

unperturbed one, and a scheme specially designed for integration of orbits instead of the Runge-Kutta method. We show that this new code permits a spectacular improvement in accuracy and computation time.

AMS(MOS) subject classification: 65L05

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