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

Subject Areas : International Journal of Mathematical Modelling & Computations

Atefeh  Armand ¹ (Dep. Math, Yadegar imam khomeini (rah) shahre Rey, IAU)
Zienab  Gouyandeh ² (Dep. Math, Najaf Abad, IAU)

Received: 2017-12-15 Accepted : 2018-10-06 Published : 2017-11-01

Keywords: Nonlinear integro-differential equation, Tau-Collocation method, Matrix representation, Population model, Collocation point,

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.