SIAM Journal on Numerical Analysis
Solving ordinary differential equations I (2nd revised. ed.): nonstiff problems
Solving ordinary differential equations I (2nd revised. ed.): nonstiff problems
High-order symplectic Runge-Kutta-Nystro¨m methods
SIAM Journal on Scientific Computing
On the numerical integration of orbital problems with high order Runge-Kutta-Nyström methods
Applied Numerical Mathematics
New methods for oscillatory problems based on classical codes
Applied Numerical Mathematics
The performance of phase-lag enhanced explicit Runge-Kutta Nyström pairs on N-body problems
Journal of Computational and Applied Mathematics
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Most of the codes specially designed for the numerical integration of differential equations whose solution is near to a sinusoidal are capable of exactly integrating harmonic oscillators. This fact imposes the evaluation of complex functions for the computation of their coefficients which increases the computational cost when they are implemented in variable step-size. Recently, Garcia et al. have developed methods of Runge-Kutta-Nyström type for the numerical integration of oscillatory problems whose coefficients have a simple dependence on the step-size. In this paper, we present an embedded eighth order method of this type. The method obtained is competitive when comparing with classical and special codes.