On a finite difference scheme for a Beeler-Reuter based model of cardiac electrical activity

Monica Hanslien; Kenneth H. Karlsen; Aslak Tveito; Xue-Cheng Tai

On a finite difference scheme for a Beeler-Reuter based model of cardiac electrical activity

Monica Hanslien
, Kenneth H. Karlsen
, Aslak Tveito
, Xue-Cheng Tai

Department of Mathematics

Research output: Contribution to journal › Journal article › peer-review

5 Citations (Scopus)

Abstract

We investigate an explicit finite difference scheme for a Beeler-Reuter based model of cardiac electrical activity. As our main result, we prove that the finite difference solutions are bounded in the L^∞-norm. We also prove the existence of a weak solution by showing convergence to the solutions of the underlying model as the discretization parameters tend to zero. The convergence proof is based on the compactness method.

Original language	English
Pages (from-to)	395-412
Number of pages	18
Journal	International Journal of Numerical Analysis and Modeling
Volume	3
Issue number	4
Publication status	Published - Dec 2006

User-Defined Keywords

reaction-diffusion system of Beeler-Reuter type
excitable cells
cardiac electric field
monodomain model
finite difference scheme
maximum principle
convergence

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http://www.math.ualberta.ca/ijnam/Volume-3-2006/No-4-06/2006-04-02.pdf

Cite this

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title = "On a finite difference scheme for a Beeler-Reuter based model of cardiac electrical activity",

abstract = "We investigate an explicit finite difference scheme for a Beeler-Reuter based model of cardiac electrical activity. As our main result, we prove that the finite difference solutions are bounded in the L∞-norm. We also prove the existence of a weak solution by showing convergence to the solutions of the underlying model as the discretization parameters tend to zero. The convergence proof is based on the compactness method.",

keywords = "reaction-diffusion system of Beeler-Reuter type, excitable cells, cardiac electric field, monodomain model, finite difference scheme, maximum principle, convergence",

author = "Monica Hanslien and Karlsen, \{Kenneth H.\} and Aslak Tveito and Xue-Cheng Tai",

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AU - Hanslien, Monica

AU - Karlsen, Kenneth H.

AU - Tveito, Aslak

AU - Tai, Xue-Cheng

N1 - Funding Information: This research was supported by the BeMatA program of The Research Council of Norway.

PY - 2006/12

Y1 - 2006/12

N2 - We investigate an explicit finite difference scheme for a Beeler-Reuter based model of cardiac electrical activity. As our main result, we prove that the finite difference solutions are bounded in the L∞-norm. We also prove the existence of a weak solution by showing convergence to the solutions of the underlying model as the discretization parameters tend to zero. The convergence proof is based on the compactness method.

AB - We investigate an explicit finite difference scheme for a Beeler-Reuter based model of cardiac electrical activity. As our main result, we prove that the finite difference solutions are bounded in the L∞-norm. We also prove the existence of a weak solution by showing convergence to the solutions of the underlying model as the discretization parameters tend to zero. The convergence proof is based on the compactness method.

KW - reaction-diffusion system of Beeler-Reuter type

KW - excitable cells

KW - cardiac electric field

KW - monodomain model

KW - finite difference scheme

KW - maximum principle

KW - convergence

UR - https://www.scopus.com/pages/publications/34547553080

M3 - Journal article

AN - SCOPUS:34547553080

SN - 1705-5105

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SP - 395

EP - 412

JO - International Journal of Numerical Analysis and Modeling

JF - International Journal of Numerical Analysis and Modeling

IS - 4

ER -

On a finite difference scheme for a Beeler-Reuter based model of cardiac electrical activity

Abstract

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