The Tau-Collocation Method for Solving Nonlinear Integro-Dierential Equations and Application of a Population Model

This paper present a computational technique that called Tau-collocation method for the developed solution of nonlinear integro-dierential equations which involves a population model. To do this, the nonlinear integro-dierential equations are transformed into a system of linear algebraic equations in matrix form without interpolation of non polynomial terms of equations. Then, using collocation points, we solve this system and obtain the unknown coecients. To illustrate the ability and reliability of the method some nonlinear integro-dierential equations and population models are presented. The results reveal that the method is very eective and simple.