Wavelets method for solving nonlinear stochastic Itô–Volterra integral equations

Author:

Heydari Mohammad Hossein1,Hooshmandasl Mohammad Reza2,Cattani Carlo3

Affiliation:

1. Department of Mathematics, Shiraz University of Technology, Shiraz, Iran

2. Faculty of Mathematics, Yazd University, Yazd, Iran

3. Engineering School, Tuscia University, Largo dell’s University, 01100Viterbo, Italy

Abstract

AbstractIn 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.

Publisher

Walter de Gruyter GmbH

Subject

General Mathematics

Reference72 articles.

1. Numerical solution of stochastic Volterra integral equations by a stochastic operational matrix based on block pulse functions;Math. Comput. Model.,2012

2. A good approximate solution for Liénard equation in a large interval using block pulse functions;J. Math. Ext.,2013

3. Wavelets method for solving systems of nonlinear singular fractional Volterra integro-differential equations;Commun. Nonlinear Sci. Numer. Simul.,2014

4. Adaptive explicit-implicit tau-leaping method with automatic tau selection;J. Chem. Phys.,2007

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