Special Seminar in Applied Mathematics

In this talk we will provide an overview of theory and application of exponential propagation iterative methods of Runge-Kutta-type (EPIRK). In recent years exponential integrators emerged as an efficient alternative to implicit methods for solving large stiff systems of differential equations. We will introduce the EPIRK framework that allows construction of particularly efficient exponential schemes. The flexibility of the EPIRK methods enables construction of time integrators suited for several classes of problems depending on the structure of the stiff operator. Both classical and stiffly accurate methods can be derived and their convergence can be proved. We will discuss the building blocks that make up an efficient exponential integrator and illustrate performance advantages of such schemes using numerical examples. In addition, we will discuss a new software package EPIC in which exponential integrators are implemented for serial and parallel computing platforms.