Shifted Legendre Tau Method for Solving the Stochastic Weakly Singular Integro-Differential Equations

‎In this paper‎, ‎the stochastic weakly singular integro-differential equation is discussed‎. ‎The shifted Legendre Tau method is introduced for finding the unknown function‎. ‎For this purpose‎, ‎shifted Legendre polynomials and their properties are introduced‎. ‎The proposed method is based on expanding the approximate solution as the elements of shifted Legendre polynomials‎. ‎We reduce the problem to set of algebraic equations by using operational matrices‎. ‎Also the convergence analysis of shifted Legendre polynomials and error estimation for this method have been discussed‎. ‎Finally‎, ‎several numerical examples are given to demonstrate the high accuracy of the method‎.