On a finite difference scheme for a Beeler-Reuter based model of cardiac electrical activity
Monica Hanslien 1, Kenneth H. Karlsen 2, Aslak Tveito 11 Department of Scientific Computing, Simula Research Laboratory, P.O.Box 134, N-1325 Lysaker, Norway
2 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
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: firstname.lastname@example.org (M. Hanslien), email@example.com (K. H. Karlsen), firstname.lastname@example.org (A. Tveito)