Year: 2006
International Journal of Numerical Analysis and Modeling, Vol. 3 (2006), Iss. 4 : pp. 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.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/2006-IJNAM-910
International Journal of Numerical Analysis and Modeling, Vol. 3 (2006), Iss. 4 : pp. 395–412
Published online: 2006-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 18
Keywords: reaction-diffusion system of Beeler-Reuter type excitable cells cardiac electric field monodomain model finite difference scheme maximum principle convergence.