  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.
