TY - JOUR
T1 - Stability of Two-Integrators for the Aliev-Panfilov System
AU - Hanslien , M.
AU - Artebrant , R.
AU - Tveito , A.
AU - Lines , G. T.
AU - Cai , X.
JO - International Journal of Numerical Analysis and Modeling
VL - 3
SP - 427
EP - 442
PY - 2011
DA - 2011/08
SN - 8
DO - http://doi.org/
UR - https://global-sci.org/intro/article_detail/ijnam/694.html
KW - reaction-diffusion system, implict Runge-Kutta, electrocardiology.
AB - <p style="text-align: justify;">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.<br/>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.</p>