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DOI: 10.46698/n8076-2608-1378-r

New Numerical Method for Solving Nonlinear Stochastic Integral Equations

Zeghdane, R.
Vladikavkaz Mathematical Journal 2020. Vol. 22. Issue 4.
Abstract:
The purpose of this paper is to propose the Chebyshev cardinal functions for solving Volterra stochastic integral equations. The method is based on expanding the required approximate solution as the element of Chebyshev cardinal functions. Though the way, a new operational matrix of integration is derived for the mentioned basis functions. More precisely, the unknown solution is expanded in terms of the Chebyshev cardinal functions including undetermined coefficients. By substituting the mentioned expansion in the original problem, the operational matrix reducing the stochastic integral equation to system of algebraic equations. The convergence and error analysis of the etablished method are investigated in Sobolev space. The method is numerically evaluated by solving test problems caught from the literature by which the computational efficiency of the method is demonstrated. From the computational point of view, the solution obtained by this method is in excellent agreement with those obtained by other works and it is efficient to use for different problems.
Keywords: Chebyshev cardinal functions, stochastic operational matrix, Brownian motion, Ito integral, collocation method, numerical solution
Language: English Download the full text  
For citation: Zeghdane, R. New Numerical Method for Solving Nonlinear Stochastic Integral Equations, Vladikavkaz Math. J., 2020, vol. 22, no. 4, pp.68-86. DOI 10.46698/n8076-2608-1378-r
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