Recently, systems of coupled renewal and retarded functional differential equations have begun to play a central role in complex and realistic models of population dynamics. In view of studying the local asymptotic stability of equilibria and (mainly) periodic solutions, we propose a pseudospectral collocation method to approximate the eigenvalues of the evolution operators of linear coupled equations, providing rigorous error and convergence analyses and numerical tests. The method combines the ideas of the analogous techniques developed separately for renewal equations and for retarded functional differential equations. Coupling them is not trivial, due to the different state spaces of the two classes of equations, as well as to their different regularization properties.

最近，耦合更新和滞后泛函微分方程组的系统已开始在复杂而现实的人口动态模型中发挥中心作用。考虑到研究平衡点和（主要）周期解的局部渐近稳定性，我们提出了一种伪谱配点方法来逼近线性耦合方程组演化算子的​​特征值，提供了严格的误差和收敛性分析以及数值测试。该方法结合了分别为更新方程和滞后泛函微分方程开发的类似技术的思想。由于两类方程的状态空间不同以及它们的正则化性质不同，因此将它们耦合起来并非易事。