Two Step Runge-Kutta-Nyström Methods for Oscillatory Problems Based on Mixed Polynomials

Using the linear stage representation, we describe how to derive two step Runge-Kutta-Nystrom methods which integrate trigonometric and mixed polynomials exactly

Beatrice Paternoster

2007

Scholarcy highlights

  • We are concerned with the second order initial value problem y = f), y(t0) = y0, y = y0, y(t), f ∈ Rn,having periodic or oscillatory solutions, which describes many processes in technical sciences
  • In this paper we consider two step Runge–Kutta–Nystrom methods for having periodic or oscillatory solutions, for which a good estimate of the frequency is known in advance
  • We treat formulas by extending Albrecht’s technique to the numerical method we considered, as in previous research
  • We can consider TSRKN methods which integrate ODEs having periodic or oscillatory solutions, which can be expressed through trigonometric polynomials
  • In this paper we design the approach to be used in the derivation of two step Runge–Kutta–Nystrom methods in the case that only one frequency is fitted, but the development of TSRKN methods in which more frequencies are fitted can be considered as well
  • Some authors addressed the problem of how choosing the optimal value of the frequency to predict, and this new perspective enlarges the sphere of application of methods with ν–dependent parameters, where ν is given by the product of the fitted frequency and the stepsize

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