Computational Simulation of the Lotka One-Sex Population Model Applying the Stabilized MLS-Galerkin Method

The Lotka one-sex population model as a continuous time population model, governed by the Euler–Lotka integral equation, is a pivotal mathematical framework in ecology. This paper aims to explore a computational method for solving Euler–Lotka integral equations with the net maternity function as the kernel which can be either continuous or logarithmic. This approach utilizes the capabilities of the stabilized moving least squares (MLS) approximation, as a meshless local technique, created by applying scattered data points within the context of the discrete Galerkin method. The stabilized MLS method is not affected by the distance between points, unlike the traditional MLS method, which experiences reduced stability as the distance between points decreases. Furthermore, we evaluate the error for the developed technique. The effectiveness and reliability of this newly offered approach are evaluated through various Euler–Lotka integral equations.