This paper deals with the approximate solution of nonlinear stochastic Itô–Volterra integral equations (NSIVIE). First, the solution domain of these nonlinear integral equations is divided into a finite number of subintervals. Then, the Chebyshev–Gauss–Radau points along with the Lagrange interpolation method are employed to get approximate solution of NSIVIE in each subinterval. The method enjoys the advantage of providing the approximate solutions in the entire domain accurately. The convergence analysis of the numerical method is also provided. Some illustrative examples are given to elucidate the efficiency and applicability of the proposed method.
Numerical Treatment of Nonlinear Stochastic Itô–Volterra Integral Equations by Piecewise Spectral-Collocation Method
Contributed by the Design Engineering Division of ASME for publication in the JOURNAL OF COMPUTATIONAL AND NONLINEAR DYNAMICS. Manuscript received October 5, 2018; final manuscript received December 21, 2018; published online January 22, 2019. Assoc. Editor: Dumitru Baleanu.
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Mohammadi, F. (January 22, 2019). "Numerical Treatment of Nonlinear Stochastic Itô–Volterra Integral Equations by Piecewise Spectral-Collocation Method." ASME. J. Comput. Nonlinear Dynam. March 2019; 14(3): 031007. https://doi.org/10.1115/1.4042440
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