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Trigonometrically fitted two-step hybrid methods for special second order ordinary differential equations. (English) Zbl 1210.65133
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:
65L06Multistep, Runge-Kutta, and extrapolation methods
65L05Initial value problems for ODE (numerical methods)
34A34Nonlinear ODE and systems, general
65L20Stability and convergence of numerical methods for ODE
34C10Qualitative theory of oscillations of ODE: zeros, disconjugacy and comparison theory
34C25Periodic solutions of ODE
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