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.

我们在本文中的目的是提出一种搭配方法，以解决单个物种和相互作用物种的两个种群模型。为此，研究了物流增长模型和猎物-捕食者模型。这些模型通过Pell-Lucas搭配方法进行数值求解。该方法以截短的Pell-Lucas级数的形式给出了这些模型的近似解。通过使用Pell-Lucas搭配方法，将非线性数学模型转换为非线性代数方程组。解决了该非线性方程组，获得的系数是截断的Pell-Lucas serie解的系数。此外，残差校正方法用于找到更好的近似解。所有结果均显示在表格和图表中$（ñ，\mathrm{中号}）$值，并使用其他方法进行比较。可以看出，该方法对所提出的模型问题给出了有效的结果。