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Title: 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 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(1/(n{sup 2}) ). 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.
Authors:
 [1] ;  [2] ;  [1] ;  [2] ;  [1] ;  [2] ;  [3]
  1. Faculty of Mathematics, Yazd University, Yazd (Iran, Islamic Republic of)
  2. (Iran, Islamic Republic of)
  3. Department of Mathematics, University of Salerno, Fisciano (Italy)
Publication Date:
OSTI Identifier:
22314883
Resource Type:
Journal Article
Resource Relation:
Journal Name: Journal of Computational Physics; Journal Volume: 270; Other Information: Copyright (c) 2014 Elsevier Science B.V., Amsterdam, The Netherlands, All rights reserved.; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; ACCURACY; BROWNIAN MOVEMENT; COMPARATIVE EVALUATIONS; CONVERGENCE; INTEGRALS; MATRICES; PULSES; RELIABILITY; STOCHASTIC PROCESSES; VOLTERRA INTEGRAL EQUATIONS