We present a novel method for solving ordinary differential equations (ODEs) while preserving all polynomial first integrals. The method is essentially a symplectic Runge-Kutta method applied to a reformulated version of the ODE under study and is illustrated through a number of examples including Hamiltonian ODEs, a Nambu system and the Toda Lattice. When applied to certain Hamiltonian ODEs, the proposed method yields the averaged vector field method as a special case.

翻译：我们提出了一个解决普通差异方程式的新颖方法,同时保留所有多边第一组合体。这种方法基本上是用于正在研究的重塑版ODE的共振龙格-库塔法,通过包括汉密尔顿式ODEs、Nambu系统和Toda Lattice在内的若干例子加以说明。在适用于某些汉密尔顿式ODEs时,拟议方法将平均矢量场法作为特例产生。