Volume 5, Issue 4
High-Order Compact Difference Methods for Simulating wave Propagations
in Excitable Media.

Zichen Deng

DOI:

Int. J. Numer. Anal. Mod. B,5 (2014), pp. 339-346

Published online: 2014-05

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  • Abstract

In this paper, we present a study of some high-order compact difference schemes for solving the Fitzhugh-Nagumo equations governed by two coupled time-dependent nonlinear reaction diffusion equations in two variables. Solving the Fitzhugh-Nagumo equations is quite challenging, since the equations involve spatial and temporal dynamics in two different scales and the solutions exhibit shock-like waves. The numerical schemes employed have sixth order accuracy in space, and fourth order in time if the fourth order Runge-Kutta method is adopted for time marching. To improve effciency, we also propose an ADI scheme (for two dimensional problems), which has second order accuracy in time. Numerical results are presented for plane wave propagation in one dimension and spiral waves for two dimensions.

  • Keywords

Spiral waves excitable medium FitzHugh-Nagumo equations compact difference methods

  • AMS Subject Headings

65M06 92B05 35Q92

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{IJNAMB-5-339, author = {Zichen Deng}, title = {High-Order Compact Difference Methods for Simulating wave Propagations
in Excitable Media.}, journal = {International Journal of Numerical Analysis Modeling Series B}, year = {2014}, volume = {5}, number = {4}, pages = {339--346}, abstract = {In this paper, we present a study of some high-order compact difference schemes for solving the Fitzhugh-Nagumo equations governed by two coupled time-dependent nonlinear reaction diffusion equations in two variables. Solving the Fitzhugh-Nagumo equations is quite challenging, since the equations involve spatial and temporal dynamics in two different scales and the solutions exhibit shock-like waves. The numerical schemes employed have sixth order accuracy in space, and fourth order in time if the fourth order Runge-Kutta method is adopted for time marching. To improve effciency, we also propose an ADI scheme (for two dimensional problems), which has second order accuracy in time. Numerical results are presented for plane wave propagation in one dimension and spiral waves for two dimensions.}, issn = {}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/ijnamb/238.html} }
TY - JOUR T1 - High-Order Compact Difference Methods for Simulating wave Propagations
in Excitable Media. AU - Zichen Deng JO - International Journal of Numerical Analysis Modeling Series B VL - 4 SP - 339 EP - 346 PY - 2014 DA - 2014/05 SN - 5 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/ijnamb/238.html KW - Spiral waves KW - excitable medium KW - FitzHugh-Nagumo equations KW - compact difference methods AB - In this paper, we present a study of some high-order compact difference schemes for solving the Fitzhugh-Nagumo equations governed by two coupled time-dependent nonlinear reaction diffusion equations in two variables. Solving the Fitzhugh-Nagumo equations is quite challenging, since the equations involve spatial and temporal dynamics in two different scales and the solutions exhibit shock-like waves. The numerical schemes employed have sixth order accuracy in space, and fourth order in time if the fourth order Runge-Kutta method is adopted for time marching. To improve effciency, we also propose an ADI scheme (for two dimensional problems), which has second order accuracy in time. Numerical results are presented for plane wave propagation in one dimension and spiral waves for two dimensions.
Zichen Deng. (1970). High-Order Compact Difference Methods for Simulating wave Propagations
in Excitable Media.. International Journal of Numerical Analysis Modeling Series B. 5 (4). 339-346. doi:
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