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A Runge-Kutta-Nyström method for the numerical integration of special second-order periodic initial-value problems. (English) Zbl 0872.65066

Summary: A new Runge-Kutta-Nyström method is developed to integrate second-order differential equations of the form \(u''(t)= f(t,u)\) when they posses an oscillatory solution. Through an appropriate definition of the parameters of the method, a fourth algebraic order is obtained and the phase-lag is reduced significantly.

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
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