A computational method for solving stochastic Itô–Volterra integral equations based on stochastic operational matrix for generalized hat basis functions

In this paper, a new computational method based on the generalized hat basis functions is proposed for solving stochastic Itô–Volterra integral equations. In this way, a new stochastic operational matrix for generalized hat functions on the finite interval [0,T] is obtained. By using these basis fun...

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Bibliographic Details
Published in:Journal of computational physics 2014-08, Vol.270, p.402-415
Main Authors: Heydari, M.H., Hooshmandasl, M.R., Maalek Ghaini, F.M., Cattani, C.
Format: Article
Language:English
Subjects:
ACCURACY
Basis functions
Blocking
Brownian motion process
BROWNIAN MOVEMENT
CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS
COMPARATIVE EVALUATIONS
Computation
CONVERGENCE
Generalized hat basis functions
Integral equations
INTEGRALS
Itô integral
Mathematical analysis
Mathematical models
MATRICES
PULSES
RELIABILITY
Stochastic Itô–Volterra integral equations
Stochastic operational matrix
STOCHASTIC PROCESSES
Stochasticity
Texts
VOLTERRA INTEGRAL EQUATIONS
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Summary:In this paper, a new computational method based on the generalized hat basis functions is proposed for solving stochastic Itô–Volterra integral equations. In this way, a new stochastic operational matrix for generalized hat functions on the finite interval [0,T] is obtained. By using these basis functions and their stochastic operational matrix, such problems can be transformed into linear lower triangular systems of algebraic equations which can be directly solved by forward substitution. Also, the rate of convergence of the proposed method is considered and it has been shown that it is O(1n2). Further, in order to show the accuracy and reliability of the proposed method, the new approach is compared with the block pulse functions method by some examples. The obtained results reveal that the proposed method is more accurate and efficient in comparison with the block pule functions method.
ISSN:0021-9991
1090-2716
DOI:10.1016/j.jcp.2014.03.064