## On the numerical integration of second-order initial value problems with a periodic forcing function.(English)Zbl 0589.65064

Runge-Kutta-Nyström type methods and special predictor-corrector methods are constructed for the accurate solution of second-order differential equations of which the solution is dominated by the forced oscillation originating from an external, periodic forcing term. For a family of second-order explicit and linearly implicit Runge-Kutta- Nyström methods it is shown that the forced oscillation is represented with zero phase lag. For a family of predictor-corrector methods of fourth-order, it is shown that both the phase lag order and the dissipation of the forced oscillation can be made arbitrarily high. Numerical examples illustrate the effectiveness of our reduced phase lag methods.

### MSC:

 65L05 Numerical methods for initial value problems involving ordinary differential equations 34A34 Nonlinear ordinary differential equations and systems
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### References:

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