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Georgian Mathematical Journal

Editor-in-Chief: Kiguradze, Ivan / Buchukuri, T.

Editorial Board: Kvinikadze, M. / Bantsuri, R. / Baues, Hans-Joachim / Besov, O.V. / Bojarski, B. / Duduchava, R. / Engelbert, Hans-Jürgen / Gamkrelidze, R. / Gubeladze, J. / Hirzebruch, F. / Inassaridze, Hvedri / Jibladze, M. / Kadeishvili, T. / Kegel, Otto H. / Kharazishvili, Alexander / Kharibegashvili, S. / Khmaladze, E. / Kiguradze, Tariel / Kokilashvili, V. / Krushkal, S. I. / Kurzweil, J. / Kwapien, S. / Lerche, Hans Rudolf / Mawhin, Jean / Ricci, P.E. / Tarieladze, V. / Triebel, Hans / Vakhania, N. / Zanolin, Fabio

IMPACT FACTOR 2018: 0.551

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New approximate solutions to electrostatic differential equations obtained by using numerical and analytical methods

Necdet BildikORCID iD: http://orcid.org/0000-0002-8852-5981 / Sinan DenizORCID iD: http://orcid.org/0000-0002-8884-3680
Published Online: 2018-03-03 | DOI: https://doi.org/10.1515/gmj-2018-0012


In this paper, we implement the optimal homotopy asymptotic method to find the approximate solutions of the Poisson–Boltzmann equation. We also use the results of the conjugate gradient method for comparison with those of the optimal homotopy asymptotic method. Our study reveals that the optimal homotopy asymptotic method gives more effective results than conjugate gradient algorithms for the considered problems.

Keywords: Optimal homotopy asymptotic method; conjugate gradient method; Poisson–Boltzmannequation; electrostatic differential equation

MSC 2010: 65L99; 74G10; 65Z05


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About the article

Received: 2015-11-09

Revised: 2016-05-12

Accepted: 2016-07-07

Published Online: 2018-03-03

This work is supported by the Scientific and Technological Research Council of Turkey (TUBITAK).

Citation Information: Georgian Mathematical Journal, ISSN (Online) 1572-9176, ISSN (Print) 1072-947X, DOI: https://doi.org/10.1515/gmj-2018-0012.

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