Applied Mathematics & Information Sciences

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In this paper, a new modified Runge-Kutta-Nystr¨om method of third algebraic order is developed. The new modified RKN method has phase-lag and amplification error of order infinity, also the first derivative of the phase lag is of order infinity. Numerical results indicate that the new method presented in this paper, is much more efficient than other methods of the same algebraic order, for the numerical integration of orbital problems.

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