### About solving stochastic It\^{o}-Volterra integral equations using the spectral collocation method

Document Type : Research Paper

Authors

Department of Mathematics, Faculty of Mathematical Sciences and Computer, Kharazmi University, Tehran, Iran

Abstract

The purpose of this paper is to propose the spectral collocation method to solve linear and nonlinear stochastic It^o-Volterra integral equations (SVIEs). The proposed approach is different from other numerical techniques as we consider the Legendre Gauss type quadrature for estimating It^o integrals. The main characteristic of the presented method is that it reduces SVIEs into a system of algebraic equations. Thus, we can solve the problem by Newton's method. Furthermore,  the convergence analysis of the approach is established. The method is computationally attractive, and to reveal the accuracy, validity, and efficiency of the proposed method, some numerical examples and convergence analysis are included.

Keywords

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###### Volume 12, Issue 2November 2021Pages 11-24
• Receive Date: 20 November 2017
• Revise Date: 08 March 2018
• Accept Date: 04 November 2019