Application of Bernoulli wavelet method for estimating a solution of linear stochastic Itô-Volterra integral equations
Multidiscipline Modeling in Materials and Structures
ISSN: 1573-6105
Article publication date: 19 December 2018
Issue publication date: 18 April 2019
Abstract
Purpose
The purpose of this paper is to develop a new method based on operational matrices of Bernoulli wavelet for solving linear stochastic Itô-Volterra integral equations, numerically.
Design/methodology/approach
For this aim, Bernoulli polynomials and Bernoulli wavelet are introduced, and their properties are expressed. Then, the operational matrix and the stochastic operational matrix of integration based on Bernoulli wavelet are calculated for the first time.
Findings
By applying these matrices, the main problem would be transformed into a linear system of algebraic equations which can be solved by using a suitable numerical method. Also, a few results related to error estimate and convergence analysis of the proposed scheme are investigated.
Originality/value
Two numerical examples are included to demonstrate the accuracy and efficiency of the proposed method. All of the numerical calculation is performed on a personal computer by running some codes written in MATLAB software.
Keywords
Acknowledgements
The authors would like to express gratitude to the editor and anonymous reviewers for their valuable comments and constructive suggestions which have helped to improve the quality and presentation of this paper.
Citation
Mirzaee, F. and Samadyar, N. (2019), "Application of Bernoulli wavelet method for estimating a solution of linear stochastic Itô-Volterra integral equations", Multidiscipline Modeling in Materials and Structures, Vol. 15 No. 3, pp. 575-598. https://doi.org/10.1108/MMMS-04-2018-0075
Publisher
:Emerald Publishing Limited
Copyright © 2018, Emerald Publishing Limited