Exponential Time Integration of Evolution Equations

The time discretization of semilinear parabolic problems requires integrators that treat the stiff part in an implicit way. Traditionally, linearly implicit methods had been used for this purpose. More recently, exponential integrators proved to be competitive for this kind of problems. In this short note, we will put emphasis on methods that linearize the problem along the numerical trajectory. We will show that the error analysis can be carried out in the framework of logarithmic matrix norms which gives rise to convergence results that are independent of the spatial grid size.