Analysis of numerical schemes of a mathematical model for sickle cell depolymerization

摘要

The purpose of this paper is to present and discuss numerical schemes for a mathematical model that describes carbon monoxide mediated sickle cell polymer melting. Two Runge–Kutta methods are analyzed and shown to be unstable by calculating the first failure value of step size and displaying the bifurcation diagram of RK4. Two nonstandard finite difference (NSFD) schemes are proposed and analyzed; one is shown to be stable subject to a predictable bound on step size, while the second one is unconditionally stable.