Application of Bernoulli wavelet method for estimating a solution of linear stochastic Itô-Volterra integral equations. Issue 3 (19th December 2018)

• Record Type: Journal Article
• Authors: Mirzaee, Farshid; Samadyar, Nasrin
• Is Part Of: Multidiscipline modeling in materials and structures. Volume 15:Issue 3(2019)
• Page Start: 575
• Page End: 598
• Publication Date: 2018-12-19
• Subjects: Linear stochastic Itô-Volterra integral equations -- Stochastic operational matrix -- Bernoulli polynomials -- Wavelet -- Brownian motion process; 60H20 -- 11B68 -- 65T60 -- 60J65; Materials -- Mathematical models -- Periodicals; Engineering -- Mathematical models -- Periodicals; 620.11015118
• DOI: 10.1108/MMMS-04-2018-0075
• Languages: English
• ISSNs: 1573-6105

Abstract

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.