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

International Journal of Mathematical Modelling & Computations

مقاله 3، دوره 7، 4 (FALL) - شماره پیاپی 28، بهمن 2017، صفحه 265-276   

نوع مقاله: Full Length Article

نویسندگان

Atefeh Armand^{* 1}؛ Zienab Gouyandeh²

¹Dep. Math, Yadegar imam khomeini (rah) shahre Rey, IAU

²Dep. Math, Najaf Abad, IAU

چکیده

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.

کلیدواژه‌ها

Nonlinear integro-differential equation؛ Tau-Collocation method؛ Matrix representation؛ Population model؛ Collocation point