A second-order finite difference approximation for a mathematical model of erythropoiesis



We present a second-order finite difference scheme for approximating solutions of a mathematical model of erythropoiesis, which consists of two nonlinear partial differential equations and one nonlinear ordinary differential equation. We show that the scheme achieves second-order accuracy for smooth solutions. We compare this scheme to a previously developed first-order method and show that the first order method requires significantly more computational time to provide solutions with similar accuracy. We also compare this numerical scheme with other well-known second-order methods and show that it has better capability in approximating discontinuous solutions. Finally, we present an application to recovery after blood loss. © 2013 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2013