Stability and convergence of a finite volume method for two systems of reaction-diffusion equations in electro-cardiology

The monodomain equations model the propagation of the action potential in the human heart: a very sharp pulse propagating at a high speed, whose computation requires fine unstructured 3D meshes. It is a non-linear parabolic PDE of reaction-diffusion type, coupled to one or several ODE, with multiple time-scales.Numerical difficulties, such as unstructured meshes and stability are addressed here through the use of a finite volume method. Stability conditions are given for two time-stepping methods, and two example sets of ODEs, convergence is proved and error estimates are computed.