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Volume 8, Issue 3
Stability of Two-Integrators for the Aliev-Panfilov System

M. Hanslien, R. Artebrant, A. Tveito, G. T. Lines & X. Cai

Int. J. Numer. Anal. Mod., 8 (2011), pp. 427-442.

Published online: 2011-08

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  • Abstract

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.

  • Keywords

reaction-diffusion system, implict Runge-Kutta, electrocardiology.

  • AMS Subject Headings

92C45, 65C20, 68U20, 65L20

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{IJNAM-8-427, author = {Hanslien , M.Artebrant , R.Tveito , A.Lines , G. T. and Cai , X.}, title = {Stability of Two-Integrators for the Aliev-Panfilov System}, journal = {International Journal of Numerical Analysis and Modeling}, year = {2011}, volume = {8}, number = {3}, pages = {427--442}, abstract = {

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.

}, issn = {2617-8710}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/ijnam/694.html} }
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 -

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.

M. Hanslien, R. Artebrant, A. Tveito, G. T. Lines & X. Cai. (1970). Stability of Two-Integrators for the Aliev-Panfilov System. International Journal of Numerical Analysis and Modeling. 8 (3). 427-442. doi:
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