S. Novo and J. Rojo
Some remarks on an ODE-solver
of Kirchgraber
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
Preprint file as PDF somere.pdf