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Context. The paper presents a computational scheme and a number of techniques for increasing the efficiency of mathematical modeling of the energy characteristics of metal clusters with vacancies. The object of the research is the process of calculating wave functions and finding eigenvalues using the Numerov and the shooting methods. Objective. The objective of the research is to improve the quality of the calculation of the wave functions of electrons in a metal cluster by using optimally selected methods and techniques in the computational scheme, to ensure the adequacy, stability and cost-effectiveness of self-consistent calculations of the energy characteristics of metal clusters by limiting the change in the electrostatic potential within a single iteration, choosing the optimal integration step and data presentation format. Method. At the modeling stage, to increase the efficiency, the electron Density Functional Theory was used in conjunction with the Kohn-Sham version for the stabilized jellium model taking into account the local density approximation for calculating the energy characteristics of nanoclusters. At the simulation stage, the one-electron wave function was calculated by “stitching” it from two parts at an empirically selected point with normalization before and after the procedure. A number of techniques have been developed to improve the quality of the simulation: calculating the optimal step, limiting changes in the electrostatic profile, managing the resulting data arrays, etc. For calculations on a supercomputer, the distribution between the flows was carried out. Results. At the modeling stage, economic models of the metal sphere with a vacancy in the center were developed. For the simulation stage, a method of stable two-sided calculation of the wave function using the shooting and the Numerov methods with the optimal step has been developed. The full computational scheme for the simulation is implemented in C ++ for calculation on a PC and on a supercomputer. The simulation results were compared with the \emph{ab-initio} calculation data and experimental data for Cs, Rb, K, Na, Li, Mg, and Al clusters with and without vacancies (calculation error < 15\ Conclusions. The developed computational scheme and modeling technique allow increasing the simulation efficiency and obtaining adequate energy characteristics of metal spherical nanoclusters with and without vacancies. Further research might focus on the modification of models and simulation techniques for the study of layered nanoscale systems. [ABSTRACT FROM AUTHOR]