Prof. Cai Li, Department of Mathematics, Northwestern Polytechnical University
520, Pao Yue-Kong Library
The FitzHugh-Nagumo (FHN) monodomain model has been used to describe the propagation of the electrical potential in the myocardial cells. A fractional FHN equation was proposed for the anomalous diffusion properties of non-uniform porous media in cardiac tissue. The tempered fractional derivative was used to describe the phenomenon of the transform from anomalous diffusion to normal diffusion caused by the limitation of the particle life or the motion space at the final stage of anomalous diffusion. A tempered fractional FHN equation is proposed to characterize the special law of electrical potential propagation in the cardiac tissue. Firstly, a Crank-Nicolson (CN) scheme is proposed, and its convergence and stability are proved. Secondly, an appropriate preconditioned method is used to accelerate computation. Finally, the physical properties of the tempered fractional derivative have been verified by some numerical examples.