The mathematical models for simulating the cardiac electrical activity consist of a system of nonlinear partial differential equations coupled with a system of stiff ordinary differential equations. Numerical simulation of this coupled system requires accurate space and time discretizations. Many time and space discretization methods have been developed in the literature to decrease the computational cost of the simulations. In this work, we present a second order algorithm in space and time that allows the use of large grids with less computational time. The algorithm is based on the Alternating Direction Implicit method and uses semi-implicit time discretization. Two-dimensional numerical results comparing the suggested scheme with the second order Crank-Nicolson-Adams-Bashforth semi-implicit scheme will be presented showing the advantages of the proposed method in terms of computational time and memory consumption.

This is a joint work with Zeinab Rammal.