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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:

65L06 Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations
65L05 Numerical methods for initial value problems involving ordinary differential equations
34A34 Nonlinear ordinary differential equations and systems
65L20 Stability and convergence of numerical methods for ordinary differential equations
65L70 Error bounds for numerical methods for ordinary differential equations
34C10 Oscillation theory, zeros, disconjugacy and comparison theory for ordinary differential equations
34C25 Periodic solutions to ordinary differential equations
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References:

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