Pell–Lucas collocation method for numerical solutions of two population models and residual correction

Journal of Taibah University for Science

Gamze Yıldırım¹  Şuayip Yüzbaşı¹ 

[1] Department of Mathematics, Faculty of Science, Akdeniz University;

关键词: collocation method;    logistic growth model;    lotka–volterra model;    non-linear differential equations and their systems;    pell–lucas polynomials;    prey and predator model;   

DOI  :  10.1080/16583655.2020.1816027

来源: DOAJ

【 摘 要 】

Our aim in this article is to present a collocation method to solve two population models for single and interacting species. For this, logistic growth model and prey–predator model are examined. These models are solved numerically by Pell–Lucas collocation method. The method gives the approximate solutions of these models in form of truncated Pell–Lucas series. By utilizing Pell–Lucas collocation method, non-linear mathematical models are converted to a system of non-linear algebraic equations. This non-linear equation system is solved and the obtained coefficients are the coefficients of the truncated Pell–Lucas serie solution. Furthermore, the residual correction method is used to find better approximate solutions. All results are shown in tables and graphs for different $(N, M) $ values, and additionally the comparisons are made with other methods from. It is seen that the method gives effective results to the presented model problems.

【 授权许可】

Unknown