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New methods for oscillatory problems based on classical codes. (English) Zbl 0998.65069
Summary: The numerical integration of differential equations with oscillatory solutions is a very common problem in many fields of the applied sciences. Some methods have been specially devised for this kind of problem. In most of them the calculation of the coefficients needs more computational effort than the classical codes because such coefficients depend on the step-size in a not simple manner. On the contrary, in this work we present new algorithms specially designed for perturbed oscillators whose coefficients have a simple dependence on the step-size. The methods obtained are competitive when comparing with classical and special codes.

MSC:
65L05Initial value problems for ODE (numerical methods)
34A34Nonlinear ODE and systems, general
34C10Qualitative theory of oscillations of ODE: zeros, disconjugacy and comparison theory