In modern conditions, hydrogen energy is of particular importance in the transition to alternative energy sources. One of the most common methods for producing hydrogen is electrolysis. In this paper, we propose a method for the numerical optimization of problems of chemical kinetics. This numerical algorithm makes it possible to find the rates of constants in near-electrode processes in accordance with the given experimental data on the yield and calculate the concentrations of substances involved in near-electrode processes at specific points in time. The numerical simulation of near-electrode processes of a functioning electrolytic cell is carried out. A comparative analysis of the calculation of the yield of hydrogen and oxygen in the process of electrolysis of a potassium hydroxide solution at a constant temperature with the values obtained in the course of a full-scale experiment is given. The results of numerical studies are in close agreement with the experimental data.