This research introduces a new method for the transition from partial to ordinary differential equations that is based on the Kolmogorov superposition theorem. In this paper, we discuss the numerical implementation of the Kolmogorov theorem and propose an approach that allows us to apply the theorem to represent partial derivatives of multivariate function as a combination of ordinary derivatives of univariate functions. We tested the method by running a numerical experiment with the Poisson equation. As a result, we managed to get a system of ordinary differential equations whose solution coincides with a solution of the initial partial differential equation.

翻译：这项研究引入了一种基于科尔莫戈罗夫叠加定理的从局部差异方程式向普通差异方程式过渡的新方法。 在本文中,我们讨论了科尔莫戈罗夫定理的数值应用,并提出了一个方法,使我们能够应用该理论来代表多种变量函数的部分衍生物,作为单体函数的普通衍生物的组合。我们通过对 Poisson 方程式进行数字实验来测试该方法。结果,我们设法找到了一种普通差异方程式系统,其解决方案与最初的局部差异方程式的解决方案相吻合。