High-Order Compact Difference Methods for Simulating wave Propagations
in Excitable Media.
in Excitable Media.
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@Article{IJNAMB-5-339,
author = {JICHUN LI AND JIANWEI LI},
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} }
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 - JICHUN LI AND JIANWEI LI 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.
in Excitable Media. AU - JICHUN LI AND JIANWEI LI 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.
JICHUN LI AND JIANWEI LI. (2014). 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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in Excitable Media.. International Journal of Numerical Analysis Modeling Series B. 5 (4). 339-346. doi: