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

Abstract

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