A new collocation method for solving some first-order differential models of biological systems

In this research paper, we propose a new collocation method (NCM) that provides significantly more accurate numerical solutions to initial value problems (IVPs) of ordinary differential equations (ODEs) models of biological systems. To evaluate the performance of our proposed method, we conduct numerical simulations on various differential model problems relevant to biological systems. Specifically, the NCM is applied to obtain more accurate numerical solutions to three different models: logistic growth, SIR, and Lotka–Volterra. Our work unequivocally demonstrates that the NCM outperforms some existing numerical approaches in the literature, thereby establishing its superior efficiency and effectiveness in addressing real-world problems in the form of first-order ODE models in the domain of computational and mathematical biology. The proposed NCM method contributes to developing advanced numerical methods for solving some biological systems models.