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Zbl 1210.65133
D'Ambrosio, R.; Ferro, M.; Paternoster, B.
Trigonometrically fitted two-step hybrid methods for special second order ordinary differential equations. (English)
[J] Math. Comput. Simul. 81, No. 5, 1068-1084 (2011). ISSN 0378-4754

Summary: The purpose of this paper is to derive two-step hybrid methods for second order ordinary differential equations with oscillatory or periodic solutions. We show the constructive technique of methods based on trigonometric and mixed polynomial fitting and consider the linear stability analysis of such methods. We then carry out some numerical experiments underlining the properties of the derived classes of methods.

MSC 2000:: *65L06 Multistep, Runge-Kutta, and extrapolation methods
65L05 Initial value problems for ODE (numerical methods)
34A34 Nonlinear ODE and systems, general
65L20 Stability of numerical methods for ODE
34C10 Qualitative theory of oscillations of ODE: Zeros, etc.
34C25 Periodic solutions of ODE

Keywords: two-step hybrid methods; trigonometrical fitting; second order ordinary differential equations; oscillatory or periodic solutions; polynomial fitting; stability; numerical experiments

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