Stability of two-integrators for the Aliev-Panfilov system
M. Hanslien 1, R. Artebrant 2, A. Tveito 3, G. Lines 3, X. Cai 31 Advanced Technology Organization, GE Oil & Gas, Eivind Lyches v 10, 1338 Sandvika, Norway.
2 COMSOL AB Tegnergatan 23 SE-111 40 Stockholm, Sweden.
3 Center for Biomedical Computing at Simula Research Laboratory, P.O.Box 134, N1325 Lysaker and Department of Informatics, University of Oslo, P.O. Box 1080, Blindern, NO-0316 Oslo, Norway.
Received by the editors February 28, 2009 and, in revised form, December 7, 2010.
We propose a second-order accurate method for computing the solutions to the Aliev-Panfilov model of cardiac excitation. This two-variable reaction-diffusion system is due to its simplicity a popular choice for modeling important problems in electrocardiology; e.g. cardiac arrhythmias. The solutions might be very complicated in structure, and hence highly resolved numerical simulations are called for to capture the fine details. Usually the forward Euler time-integrator is applied in these computations; it is very simple to implement and can be effective for coarse grids. For fine-scale simulations, however, the forward Euler method suffers from a severe time-step restriction, rendering it less efficient for simulations where high resolution and accuracy are important. We analyze the stability of the proposed second-order method and the forward Euler scheme when applied to the Aliev-Panfilov model. Compared to the Euler method the suggested scheme has a much weaker time-step restriction, and promises to be more efficient for computations on finer meshes.AMS subject classifications: 92C45, 65C20, 68U20, 65L20
Key words: reaction-diffusion system, implict Runge-Kutta, electrocardiology.
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