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research-article

Numerical treatment of nonlinear stochastic It\^o-Volterra integral equations by piecewise spectral-collocation method

[+] Author and Article Information
Fakhrodin Mohammadi

Department of Mathematics, University of Hormozgan , Bandar Abbas, P. O. Box 3995, Iran
f.mohammadi62@hotmail.com
f.mohammadi@hormozgan.ac.ir

1Corresponding author.

ASME doi:10.1115/1.4042440 History: Received October 05, 2018; Revised December 21, 2018

Abstract

This paper deals with the approximate solution of nonlinear stochastic It\^o-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 approximate solution of NSIVIE in each subinterval. The method has 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 illustrate the efficiency and applicability of the proposed method.

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