  The monodomain model is widely used in in-silico cardiology to describe
excitation propagation in the myocardium. Frequently, operator splitting is
used to decouple the stiff reaction term and the diffusion term in the
monodomain model so that they can be solved separately. Commonly, the diffusion
term is solved implicitly with a large time step while the reaction term is
solved by using an explicit method with adaptive time stepping. In this work,
we propose a fully explicit method for the solution of the decoupled monodomain
model. In contrast to semi-implicit methods, fully explicit methods present
lower memory footprint and higher scalability. However, such methods are only
conditionally stable. We overcome the conditional stability limitation by
proposing a dual adaptive explicit method in which adaptive time integration is
applied for the solution of both the reaction and diffusion terms. In a set of
numerical examples where cardiac propagation is simulated under physiological
and pathophysiological conditions, results show that our proposed method
presents preserved accuracy and improved computational efficiency as compared
to standard operator splitting-based methods.
