A phase-fitted collocation-based Runge–Kutta–Nyström method

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Abstract

We consider collocation-based Runge–Kutta–Nyström methods with symmetric points and derive a three-stage method which results exact in phase for second order linear ODEs having a periodic or an oscillatory solution. We assume that the dominant frequency k can be estimated in advance; then the resulting method depends on the parameter θ=kh, where h is the stepsize. Due to its stability properties, the method is suitable to integrate systems which exhibits a moderate stiffness. The procedure can be easily generalized to derive phase-fitted RKN methods with an arbitrary high order.

References (27)

  • K. Burrage

    Parallel and Sequential Methods for Ordinary Differential Equations

    (1995)
  • H. Brunner et al.

    The Numerical Solution of Volterra Equations

    (1996)
  • M. Cafaro et al.

    Analysis of stability of rational approximations through computer algebra

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