ISSN 1817-2172, рег. Эл. № ФС77-39410, ВАК

Differential Equations and Control Processes
(Differencialnie Uravnenia i Protsesy Upravlenia)

Mathematical Model and Numerical Scheme for Calculation of Electric Fields in Galvanic Baths with Non-conductive Screen


Irina Yu. Pchelintseva

Tambov State Technical University
Postgraduate student of the Department of Automated Decision Support Systems
ul. Sovetskaya 106, 392000, Tambov, Russian Federation

Yuriy V. Litovka

Tambov State Technical University
Doctor of Technical Sciences, Professor
Professor of the Department of Automated Decision Support Systems
ul. Sovetskaya 106, 392000, Tambov, Russian Federation


A mathematical model of the electric field in a electroplating bath with a flat anode and cathode, which has an infinitely thin flat insulator wall with transverse slots, is considered. Such a non-conductive screen is necessary for a more uniform coverage of the cathode detail. In this article, a transition is made to the difference analogue of the problem. A numerical method based on Newton's method for solving nonlinear algebraic equations is described, a computational experiment for 4 slits is carried out. The obtained results show the effectiveness of the applied numerical method.



  1. Dutov, A. V., Sypalo, K. I., Solovjev, D. S., Litovka, Y. V., Solovjeva, I. A., Nesterov, V. A. Search for the optimal control over current regimes in electroplating processes with multi anodes at a diversified assortment of treated articles // Journal of Computer and Systems Sciences International, 2019, vol. 58, no. 1, pp. 75-85
  2. Litovka, Yu. V., Mikheev, V. V. Numerical calculation of the electric field in an electroplating bath with bipolar electrodes // Theoretical Foundations of Chemical Engineering, 2006, vol. 40, no. 3, pp. 305-310
  3. Demidovich, B. P., Maron, I. A. Osnovy vychislitel'noy matematiki [Fundamentals of Computational Mathematics], Lan' Publ., St. Petersburg, 2006, 672 p
  4. Pchelintseva, I. Yu., Pchelintsev, A. N., Litovka, Yu. V. Modeling of metal distribution when coating flat metal plates in electroplating baths // International Journal of Numerical Modelling: Electronic Networks, Devices and Fields, 2021, vol. 34, iss. 2, e2830, 10 pp
  5. Kudryavtsev, N. T. Elektroliticheskiye pokrytiya metallami [Electrolytic Coating with Metals], Khimiya Publ., Moscow, 1979, 352 p
  6. Zhuk, N. P. Kurs teorii korrozii i zashchity metallov [Corrosion and Metal Protection Theory Course]. Al'yans, Moscow, 2014, 472 p
  7. Tolmachev, A. V., Konovalov, A. V., Partin, A. S. Effektivnost' algoritma LU-razlozheniya s dvukhmernym tsiklicheskim raspredeleniyem matritsy dlya parallel'nogo resheniya uprugoplasticheskoy zadachi [Efficiency of LU-decomposition algorithm with two-dimensional cyclic matrix distribution for parallel solution of elastoplastic problem] // Programmnyye produkty i sistemy, 2013, no. 3, pp. 94-99
  8. Maxima computer algebra system,
  9. Pchelintseva, I. Yu., Pchelintsev, A. N., Litovka, Yu. V. Svidetel'stvo o gosudarstvennoy registratsii programmy dlya EVM №2020614929. Chislennoye resheniye uravneniya Laplasa dlya raschota raspredeleniya elektricheskogo potentsiala v gal'vanicheskoy vanne na baze matematicheskogo paketa Maxima [Certificate of state registration of the computer program No. 2020614929. Numerical solution of the Laplace equation for calculating the distribution of electric potential in a galvanic bath based on the mathematical package Maxima]. - 04/29/2020

Full text (pdf)