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Volume 3, Issue 4
On a Finite Difference Scheme for a Beeler-Reuter Based Model of Cardiac Electrical Activity

M. Hanslien, K. H. Karlsen & A. Tveito

Int. J. Numer. Anal. Mod., 3 (2006), pp. 395-412.

Published online: 2006-03

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  • 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.

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COPYRIGHT: © Global Science Press

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@Article{IJNAM-3-395, author = {M. Hanslien, K. H. Karlsen and A. Tveito}, title = {On a Finite Difference Scheme for a Beeler-Reuter Based Model of Cardiac Electrical Activity}, journal = {International Journal of Numerical Analysis and Modeling}, year = {2006}, volume = {3}, number = {4}, pages = {395--412}, 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.

}, issn = {2617-8710}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/ijnam/910.html} }
TY - JOUR T1 - On a Finite Difference Scheme for a Beeler-Reuter Based Model of Cardiac Electrical Activity AU - M. Hanslien, K. H. Karlsen & A. Tveito JO - International Journal of Numerical Analysis and Modeling VL - 4 SP - 395 EP - 412 PY - 2006 DA - 2006/03 SN - 3 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/ijnam/910.html KW - reaction-diffusion system of Beeler-Reuter type, excitable cells, cardiac electric field, monodomain model, finite difference scheme, maximum principle, convergence. 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.

M. Hanslien, K. H. Karlsen and A. Tveito. (2006). On a Finite Difference Scheme for a Beeler-Reuter Based Model of Cardiac Electrical Activity. International Journal of Numerical Analysis and Modeling. 3 (4). 395-412. doi:
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