A combination method for numerical solution of the nonlinear stochastic Itô-Volterra integral equation

Abstract

In this article, an efficient combination approach grounded on barycentric rational interpolation and Picard iteration is proposed for solving nonlinear stochastic Itô-Volterra integral equations(SIVIEs). The presented method transforms the SIVIEs into the corresponding algebraic equations whose solution is the expansion coefficients of the barycentric rational interpolation, which is obtained by the Itô-approximation, Gauss-Legendre quadrature formula and Picard iteration algorithm. Moreover, theoretical study confirms that the error and convergence analysis of the approach. In the end, several related numerical experiments are given, which demonstrate the applicability and efficiency of the proposed technique compared with other known numerical methods.