The Veselov approach provides a discrete formulation of the Euler–Lagrange equation. To get this, a discrete Lagrangian version of a continuous one is considered and then a variational process is used. This problem has been studied in many papers by different authors, according to references and therein citations. This type of discretization can be useful in the case when the continuous Euler–Lagrange equation is given in a semispray form, which is difficult to solve effectively (as for example in the many-body problem). Our aim is to consider a given continuous Lagrangian and to construct directly discrete approximations of the corresponding Euler–Lagrange equation. This is done without considering a discrete Lagrangian and a variational process, nor by using a difference equation of geodesics. Some numerical examples are included in order to compare the performance of the proposed approximations versus the classical Veselov approach.

Veselov 方法提供了欧拉-拉格朗日方程的离散公式。为了得到这一点，考虑了连续的离散拉格朗日版本，然后使用变分过程。根据参考文献和其中的引文，不同作者在许多论文中研究了这个问题。这种类型的离散化在连续 Euler-Lagrange 方程以半喷雾形式给出的情况下很有用，这很难有效求解（例如在多体问题中）。我们的目标是考虑给定的连续拉格朗日函数并直接构造相应欧拉-拉格朗日方程的离散近似。这是在不考虑离散拉格朗日和变分过程的情况下完成的，也不使用测地线的差分方程。