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Int. J. Numer. Anal. Mod., 3 (2006), pp. 395-412. |
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On a finite difference scheme for a Beeler-Reuter based model of cardiac electrical activity Monica Hanslien 1, Kenneth H. Karlsen 2, Aslak Tveito 1 1 Department of Scientific Computing, Simula Research Laboratory, P.O.Box 134, N-1325 Lysaker, Norway2 Centre of Mathematics for Applications,University of Oslo, P.O. Box 1053, Blindern, N-0316 Oslo, Norway and Department of Scientific Computing, Simula Research Laboratory, P.O.Box 134, N-1325 Lysaker, Norway Received by the editors December, 2004 and, in revised form, April, 2005 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-infinity-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. Key words: reaction-diffusion system of Beeler-Reuter type; excitable cells; cardiac electric field; monodomain model; finite difference scheme; maximum principle; convergence Email: monicaha@simula.no (M. Hanslien), kennethk@math.uio.no (K. H. Karlsen), aslak@simula.no (A. Tveito) |