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 - <p style="text-align: justify;">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.</p>