Key result
A second-order finite difference scheme achieved second-order accuracy for smooth solutions and required significantly less computational time than a first-order method for similar accuracy.
A new second-order finite difference scheme provides more efficient and accurate approximations for mathematical models of erythropoiesis compared to existing methods.
May enhance efficiency for erythropoiesis PDE models; leaves open validation before clinical use.
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.
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Ackleh et al. (2013) studied Erythropoiesis / blood loss. Second-order finite difference scheme vs. First-order method and other second-order methods was evaluated on Computational time and accuracy for approximating solutions. A second-order finite difference scheme achieved second-order accuracy for smooth solutions and required significantly less computational time than a first-order method for similar accuracy.
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