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

Year 2019, Volume: 23 Issue: 3, 403 - 412, 01.06.2019

Elçin Gökmen Elçin Çelik

https://doi.org/10.16984/saufenbilder.410641

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.

Keywords

Continuous population models, Single and interacting species, Nonlinear differential equations and their systems, Taylor polynomials and series, Collocation points

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