标题： Kahan方法的高阶方程高次方程的类似方法 显示英文标题

标题： Analogues of Kahan's method for higher order equations of higher degree

摘要： 卡汉为具有最多二次非线性的首阶微分方程组引入了一种显式离散化方法（二次向量场）。 卡汉的方法由于能够保留原始连续系统的许多几何性质而引起了广泛关注。 特别是，已知大量二次向量场的哈密顿系统，其卡汉离散化是一个离散可积系统。 在本说明中，我们引入了一类特殊的显式保序离散化方案，这些方案适用于某些高阶和高次的常微分方程系统。 显示英文摘要

摘要： Kahan introduced an explicit method of discretization for systems of first order differential equations with nonlinearities of degree at most two (quadratic vector fields). Kahan's method has attracted much interest due to the fact that it preserves many of the geometrical properties of the original continuous system. In particular, a large number of Hamiltonian systems of quadratic vector fields are known for which their Kahan discretization is a discrete integrable system. In this note, we introduce a special class of explicit order-preserving discretization schemes that are appropriate for certain systems of ordinary differential equations of higher order and higher degree.