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

Methods for the Numerical Analysis of Boundary Value Problem of Partial Differential Equations Based on Kolmogorov Superposition Theorem