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Spectral method for solving nonlinear stochastic Itô-Volterra integral equations

Rebiha Zeghdane

Abstract



In recent years there has been a great interest in approximating integral equations by spectral methods. In this paper, an application of spectral Chebychev method to solve nonlinear Itô Volterra integral equations is explained. One of the advantage of using the spectral
methods is that the integration with arbitrary limits for the basis functions can be obtained analytically. The approach for solving nolinear Itô Volterra integral equation with Chebychev collocation points is to choose a finite dimensional space of condidate solution. We then use Lamperti transformation to transfigure the original equation into equation with constant diffusion coefficient. The method is computationally attractive and the validilty and accuracy of the presented method are demonstrated through illustrative examples.

Keywords


stochastic Volterra integral equation, approximate solution, brownian motion, Itô integral, collocation method, numerical solution, Chebychev polynomials, spectral method, Lamperti transformation.

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