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

Journal Article · Sun Feb 15 00:00:00 EST 2015 · Journal of Computational Physics

DOI:https://doi.org/10.1016/J.JCP.2014.11.042· OSTI ID:22382188

Heydari, M.H., E-mail: [e-mail] ^[1]; The Laboratory of Quantum Information Processing, Yazd University, Yazd ^[2]; Hooshmandasl, M.R., E-mail: [e-mail] ^[1]; The Laboratory of Quantum Information Processing, Yazd University, Yazd ^[2]; Cattani, C., E-mail: [e-mail] ^[3]; Maalek Ghaini, F.M., E-mail: [e-mail] ^[1]; The Laboratory of Quantum Information Processing, Yazd University, Yazd ^[2]

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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)

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.

• OSTI ID: 22382188
• Journal Information: Journal of Computational Physics, Vol. 283; Other Information: Copyright (c) 2014 Elsevier Science B.V., Amsterdam, The Netherlands, All rights reserved.; Country of input: International Atomic Energy Agency (IAEA); ISSN 0021-9991
• Country of Publication: United States
• Language: English

Related Subjects

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