Applications of splitting Methods and exponential Integrators to an electro-chemical Heart Cell Model

Abstract

In this thesis we discuss how a system of ordinary differential equations (ODE) describing electro-chemical processes in a heart cell can be solved by numerical methods. The system is stiff, and explicit numerical solvers are therefore slow. In order to overcome the stiffness, the system is split into a stiff and a non-stiff part. The split system is solved by a Strang splitting method and an exponential integrator, based on a commutator free Lie group method. We outline a theory for estimating the computational cost of a numerical method. The solvers for the split system are compared to implicit solvers for the entire system. The conclusion is that it is possible to take out two components which are responsible for the stiffness of the original system, but that more research needs to be done in order to make efficient methods which take advantage of the fact.