| Abstract: |
| The second order ordinary differential equations are commonly encountered in various fields. Some of them can be reduced to the first order ordinary differential equations with the form of separable Hamiltonian systems. For such systems structure-preserving methods, for example,
symplectic and symmetric methods are of importance. We present a sufficient condition for
a continuous stage Runge-Kutta Nystr\{o}m (RKN) method to be symplectic and symmetric. Based on Legendre polynomial expansion we show how to construct symplectic and symmetric RKN type method with a certain order in a simple way. Some numerical experiments are presented to show the efficiency of the newly obtained methods. |
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