This article addresses a collocation method based on shifted Chebyshev cardinal functions defined on the interval \([0, T],~ T>0\) , to solve stochastic delay differential equations involving a constant delay. In this method, the stochastic delay differential equation is transformed into the stochastic Itô - Volterra integral equation with constant delay, then shifted Chebyshev cardinal functions are used as basis functions to approximate the obtained stochastic Itô - Volterra integral equation with constant delay, and the obtained equation is collocated at the suitable collocation points. Then, the \(M+1\) Gauss-Legendre quadrature rule and the Itô approximation are used to approximate integral parts. Newton’s method is used to solve a generated system of algebraic equations to get the desired approximate solution. Moreover, the convergence analysis of the presented method is also established in detail. Additionally, the applicability of the proposed method is demonstrated by solving some numerical examples.
