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.
Original language | English |
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Pages (from-to) | 395-412 |
Number of pages | 18 |
Journal | International Journal of Numerical Analysis and Modeling |
Volume | 3 |
Issue number | 4 |
Publication status | Published - Dec 2006 |
Scopus Subject Areas
- Numerical Analysis
User-Defined Keywords
- reaction-diffusion system of Beeler-Reuter type
- excitable cells
- cardiac electric field
- monodomain model
- finite difference scheme
- maximum principle
- convergence