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A second‐order finite difference approximation for a mathematical model of erythropoiesis
Author(s) -
Ackleh Azmy S.,
Thibodeaux Jeremy J.
Publication year - 2013
Publication title -
numerical methods for partial differential equations
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.901
H-Index - 61
eISSN - 1098-2426
pISSN - 0749-159X
DOI - 10.1002/num.21778
Subject(s) - mathematics , nonlinear system , scheme (mathematics) , partial differential equation , order (exchange) , order of accuracy , ordinary differential equation , finite difference scheme , first order , erythropoiesis , partial derivative , differential (mechanical device) , differential equation , mathematical analysis , numerical partial differential equations , medicine , physics , finance , quantum mechanics , aerospace engineering , engineering , economics , anemia
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