A second‐order finite difference approximation for a mathematical model of erythropoiesis. Issue 6 (3rd April 2013)

• Record Type: Journal Article
• Authors: Ackleh, Azmy S.; Thibodeaux, Jeremy J.
• Is Part Of: Numerical methods for partial differential equations. Volume 29:Issue 6(2013:Nov.)
• Page Start: 1821
• Page End: 1836
• Publication Date: 2013-04-03
• Subjects: Differential equations, Partial -- Numerical solutions -- Periodicals; 515.353
• DOI: 10.1002/num.21778
• Languages: English
• ISSNs: 0749-159X

Abstract

<abstract abstract-type="main" xml:lang="en"> <title>Abstract</title> <p>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</p> </abstract>