Numerical Solution of the System of Nonlinear Fredholm Integro-Differential Equations by the Operational Tau Method with an Error Estimation

In this paper, the operational approach to the tau method is used for the numerical solution of a nonlinear fredholm integro-differential equations system and nonlinear odes with initial or boundary conditions without linearizing. an efficient error estimation of the approximate solution is also introduced. some examples are given to clarify the efficiency and high accuracy of the method.