Stochastic differential equations (SDEs) with first integrals are considered. Exact solutions of such SDEs belong to smooth manifolds with probability 1. However, numerical solutions do not belong to the manifolds, but belong to their neighborhoods due to numerical errors. The main goal of this paper is to construct modified numerical methods for solving SDEs that have first integrals. In this study, exact solutions for three SDE systems with first integrals are obtained, and the modification of numerical methods is tested on these systems.

中文翻译：

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带有第一积分的随机微分方程数值方法的修正

考虑具有第一积分的随机微分方程（SDE）。这种SDE的精确解属于概率为1的光滑流形。但是，由于数值误差，数值解不属于流形，而是属于它们的邻域。本文的主要目的是构造用于求解具有第一积分的SDE的改进数值方法。在这项研究中，获得了三个具有第一积分的SDE系统的精确解，并在这些系统上测试了数值方法的修改。