A numerical method for solving continuous population models for single and interacting species

Abstract

In this study, a numerical approach is presented to obtain the approximate solutions of continuous population models for single and interacting species. This method is essentially based on the truncated Taylor series and its matrix representations with collocation points. By using Taylor polynomials and collocation points, this method transforms population models into a matrix equation. The matrix equation corresponds to a system of nonlinear equations with the unknown Taylor coefficients. To illustrate reliability and efficiency of the method, numerical examples are presented and results are compared with the other numerical methods. Additionally, residual correction procedure is applied to estimate the absolute errors. All numerical computations have been performed on the computer algebraic system Maple 15.