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Zbl 1003.65081
Simos, T.E.
Exponentially-fitted Runge-Kutta-Nyström method for the numerical solution of initial-value problems with oscillating solutions. (English)
[J] Appl. Math. Lett. 15, No.2, 217-225 (2002). ISSN 0893-9659

The author constructs effectively a new three stage Runge-Kutta-Nyström methods of order four for $${d^2u\over dt^2}= f(t, u(x))$$ provided that the solutions are periodic or oscillating. Stability is analyzed and numerical experiments are carried out.
[Erwin Schechter (Kaiserslautern)]

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
65L70 Error bounds (numerical methods for ODE)
34C10 Qualitative theory of oscillations of ODE: Zeros, etc.
34C25 Periodic solutions of ODE

Keywords: periodic solution; oscillating solution; error bound; stability; Runge-Kutta-Nyström methods; numerical experiments

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