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Title: An efficient computational method for solving nonlinear stochastic Itô integral equations: Application for stochastic problems in physics

Because of the nonlinearity, closed-form solutions of many important stochastic functional equations are virtually impossible to obtain. Thus, numerical solutions are a viable alternative. In this paper, a new computational method based on the generalized hat basis functions together with their stochastic operational matrix of Itô-integration is proposed for solving nonlinear stochastic Itô integral equations in large intervals. In the proposed method, a new technique for computing nonlinear terms in such problems is presented. The main advantage of the proposed method is that it transforms problems under consideration into nonlinear systems of algebraic equations which can be simply solved. Error analysis of the proposed method is investigated and also the efficiency of this method is shown on some concrete examples. The obtained results reveal that the proposed method is very accurate and efficient. As two useful applications, the proposed method is applied to obtain approximate solutions of the stochastic population growth models and stochastic pendulum problem.
Authors:
 [1] ;  [2] ;  [1] ;  [2] ;  [3] ;  [1] ;  [2]
  1. Faculty of Mathematics, Yazd University, Yazd (Iran, Islamic Republic of)
  2. (Iran, Islamic Republic of)
  3. Department of Mathematics, University of Salerno, Via Ponte Don Melillo, 84084 Fisciano (Italy)
Publication Date:
OSTI Identifier:
22382188
Resource Type:
Journal Article
Resource Relation:
Journal Name: Journal of Computational Physics; Journal Volume: 283; 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; APPROXIMATIONS; BROWNIAN MOVEMENT; INTEGRAL EQUATIONS; INTEGRALS; MATRICES; MECHANICAL VIBRATIONS; NONLINEAR PROBLEMS; NUMERICAL SOLUTION; OSCILLATIONS; STOCHASTIC PROCESSES; TIME MEASUREMENT