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In this study, two reliable approaches to solving the nonlinear stochasticIt\^o-Volterra integral equation are provided. These equations have beenevaluated using the orthonormal Chelyshkov spectral collocation technique andthe orthonormal Chelyshkov spectral Galerkin method. The techniques presentedhere transform this problem into a collection of nonlinear algebraic equationsthat have been numerically solved using the Newton method. Also, theconvergence analysis has been studied for both approaches. Two illustrativeexamples have been provided to show the efficacy, plausibility, proficiency,and applicability of the current approaches.

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