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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

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Wavelets method for solving nonlinear stochastic Itô–Volterra integral equations

Mohammad Hossein Heydari / Mohammad Reza Hooshmandasl / Carlo Cattani
Published Online: 2018-02-22 | DOI: https://doi.org/10.1515/gmj-2018-0009


In this paper, a new computational method based on the Chebyshev wavelets (CWs) is proposed for solving nonlinear stochastic Itô–Volterra integral equations. In this way, a new stochastic operational matrix (SOM) for the CWs is obtained. By using these basis functions and their SOM, such problems can be transformed into nonlinear systems of algebraic equations which can be simply solved. Moreover, a new technique for computation of nonlinear terms in such problems is presented. Further error analysis of the proposed method is also investigated and the efficiency of this method is shown on some concrete examples. The obtained results reveal that the proposed method is very accurate and efficient.

Keywords: Chebyshev wavelets; stochastic operational matrix; nonlinear stochastic Itô–Volterra integral equations; Brownian motion process; stochastic population growth model

MSC 2010: 60H20


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About the article

Received: 2015-10-17

Accepted: 2016-03-23

Published Online: 2018-02-22

Citation Information: Georgian Mathematical Journal, ISSN (Online) 1572-9176, ISSN (Print) 1072-947X, DOI: https://doi.org/10.1515/gmj-2018-0009.

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