A finite volume method for solving the monodomain and
bidomain models for the electrical activity of myocardial
tissue is presented. These models consist of a parabolic
PDE and a system of a parabolic and an elliptic PDE,
respectively, for certain electric potentials, coupled to
an ODE for the gating variable. The existence and
uniqueness of the approximate solution is proved, and it
is also shown that the scheme converges to the
corresponding weak solutions for the monodomain model,
and for the bidomain model when considering diagonal
conductivity tensors. Numerical examples in two and three
space dimensions are provided, indicating experimental
rates of convergence slightly above first order for both
models.