Loftis 9504290 The object of this proposal is to use an interdisciplinary approach to develop numerical and computational methods for the next generation of models in electrophysiology. It will focus on building models to study phenomena that evolve over long time intervals in 2D and 3D geometries, such as the formation of life-threating arrhythmias in the heart. To accomplish this goal, implicit methods will be applied to the large stiff differential system of equations that establish the kinetics of transmembrane ion movement and current flow in the tissue. This research will also apply techniques of parallelization of enhance the computational performance of implicit methods in the context of electrophysiology applications.