TY - JOUR T1 - On a Finite Difference Scheme for a Beeler-Reuter Based Model of Cardiac Electrical Activity 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.