An optimized explicit Runge-Kutta-Nystrom method for the numerical solution of orbital and related periodical initial value problems

作者：Kosti A A; Anastassi Z A; Simos T E^*

来源：Computer Physics Communications, 2012, 183(3): 470-479.

DOI：10.1016/j.cpc.2011.11.002

• Numerical solution
• Initial value problems (IVPs)
• Explicit methods
• Runge-Kutta-Nystrom methods
• Dissipative error
• Phase-lag

In this work a procedure for the construction of an explicit optimized Runge-Kutta-Nystrom method with four stages and fifth algebraic order is provided. The variable coefficients of the preserved method result after nullifying the phase-lag, the dissipative error and the first derivative of the phase-lag. We can see the efficiency of the new method through its local truncation error. Furthermore, we compare the new method%26apos;s efficiency to other numerical methods. This is shown through the integration of the two-body problem with various eccentricities and of four other initial value problems.

• 出版日期2012-3