Comparison of two efficient numerical techniques based on Chelyshkov polynomial for solving stochastic It\^o-Volterra integral equation

Abstract

In this study, two reliable approaches to solving the nonlinear stochastic It\^o-Volterra integral equation are provided. These equations have been evaluated using the orthonormal Chelyshkov spectral collocation technique and the orthonormal Chelyshkov spectral Galerkin method. The techniques presented here transform this problem into a collection of nonlinear algebraic equations that have been numerically solved using the Newton method. Also, the convergence analysis has been studied for both approaches. Two illustrative examples have been provided to show the efficacy, plausibility, proficiency, and applicability of the current approaches.