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Exponentially-fitted Runge-Kutta-Nyström method for the numerical solution of initial-value problems with oscillating solutions. (English) Zbl 1003.65081
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.

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
65L70Error bounds (numerical methods for ODE)
34C10Qualitative theory of oscillations of ODE: zeros, disconjugacy and comparison theory
34C25Periodic solutions of ODE
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References:
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