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

Mingxiang Chen; Dominic P Clemence; Gregory A Gibson

doi:10.1016/j.amc.2010.02.051

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

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2 Scopus citations

Abstract

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. © 2010 Elsevier Inc. All rights reserved.

Original language	English
Pages (from-to)	1489-1500
Number of pages	12
Journal	Applied Mathematics and Computation
Volume	216
Issue number	5
DOIs	https://doi.org/10.1016/j.amc.2010.02.051
State	Published - May 1 2010

Keywords

Finite difference schemes
NSFD methods
Sickle cell melting

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10.1016/j.amc.2010.02.051

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title = "Analysis of numerical schemes of a mathematical model for sickle cell depolymerization",

abstract = "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. {\textcopyright} 2010 Elsevier Inc. All rights reserved.",

keywords = "Finite difference schemes, NSFD methods, Sickle cell melting",

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AU - Clemence, Dominic P

AU - Gibson, Gregory A

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N2 - 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. © 2010 Elsevier Inc. All rights reserved.

AB - 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. © 2010 Elsevier Inc. All rights reserved.

KW - Finite difference schemes

KW - NSFD methods

KW - Sickle cell melting

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EP - 1500

JO - Applied Mathematics and Computation

JF - Applied Mathematics and Computation

IS - 5

ER -

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

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Keywords

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