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Numerical Solution of Stochastic Ito-Volterra Integral Equations using Haar Wavelets

Part of: Stochastic analysis Numerical methods in Fourier analysis Theoretical approximation of solutions

Published online by Cambridge University Press:  20 July 2016

Fakhrodin Mohammadi
Fakhrodin Mohammadi*
Affiliation:
Department of Mathematics, Hormozgan University, P. O. Box 3995, Bandarabbas, Iran
*
*Corresponding author. Email address:f.mohammadi62@hotmail.com (F. Mohammadi)
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Abstract

This paper presents a computational method for solving stochastic Ito-Volterra integral equations. First, Haar wavelets and their properties are employed to derive a general procedure for forming the stochastic operational matrix of Haar wavelets. Then, application of this stochastic operational matrix for solving stochastic Ito-Volterra integral equations is explained. The convergence and error analysis of the proposed method are investigated. Finally, the efficiency of the presented method is confirmed by some examples.

Keywords

Ito integralStochastic Ito-Volterra integral equationsStochastic operational matrixHaar waveletsError analysis

MSC classification

Secondary: 65T60: Wavelets 60H20: Stochastic integral equations 45L05: Theoretical approximation of solutions
Type
Research Article
Information
Numerical Mathematics: Theory, Methods and Applications , Volume 9 , Issue 3 , August 2016 , pp. 416 - 431
Copyright
Copyright © Global-Science Press 2016 

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