Iterative numerical solution of non-linear integro-differential equations by the Tau method

In this paper, we try to give an iterative application of the operational Tau method [E.L. Ortiz, H. Samara, An operational approach to the Tau method for the numerical solution of non-linear differential equations, Computing 27 (1981) 15-25], for the numerical solution of non-linear integro-differential (NIDE). A simple method convert non-linear equations to linear equations, then we use the operational Tau method for the numerical solution of linearized equation iteratively. Various numerical examples illustrate the accuracy of the method.