### Investigation of the solutions of the Laplace equation in processes using steam and gas discharges with liquid electrodes

#### R. K. Galimova^{1}, M. Y. Yakupov^{2}

Annotation | For the purpose of calculation of distribution of potential in volume of electrolyte experimental data of distribution of potential of electric field on an electrolyte surface were applied. The equation which is reducing to the equation of Laplace was solved. The cylindrical system of coordinates and method of the variable directions on a differential grid were thus used under the corresponding boundary conditions. Distributions of intensity of electric field and density of electric current near microledges of a processed surface were calculated by an alternate and triangular method at the fixed border. Results of numerical calculation of processing of a microledge of a surface confirmed the fact of faster alignment of a surface at the expense of the bigger density of current at top of peak of a ledge. |
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Keywords | numerical methods, mathematical modeling, Laplace's equati\-on, potential distribution, steam-gas category, liquid electrode, electrolyte, techno\-lo\-gical process |

^{1}Associate professor of Technical Physics Chair, KNRTU-KAI named by A.N.Tupolev, Kazan; zymat@bk.ru.^{2}Associate professor of Special Mathematics Chair, KNRTU-KAI named by A.N.Tupolev, Kazan; zymat@bk.ru.

**Citation**: R. K. Galimova, M. Y. Yakupov, "[Investigation of the solutions of the Laplace equation in processes using steam and gas discharges with liquid electrodes]", Zhurnal Srednevolzhskogo matematicheskogo obshchestva,17:1 (2015) 135–139 (In Russian)