Document Type : Research Paper
Associate Professor, Mathematics and Computer Science Department, Adib mazandaran institute of higher education, Sari, Iran
Associate Professor,Mathematica and Computer Science Department, Adib mazandaran institute of higher education, Sari, Iran
School of Mathematics and Computer Science, Damghan University, Damghan, Iran
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.