Exponential integrators offer an alternative way to integrate nonlinear systems of ODEs compared to explicit and implicit methods. A particularly advantageous characteristic of exponential schemes is their efficiency in integrating large stiff systems. While first exponential schemes were introduced in early 1960's they haven't attained wide popularity since they were considered prohibitively expensive. A proposal to combine Krylov projection algorithm and exponential integration alleviated this computational constraint and was followed by a resurgence of interest in these methods. In this talk we will describe what are the building blocks in construction of an efficient exponential integrator and provide an overview of research efforts in development of competitive schemes of this type. We will discuss such important aspects of these methods as derivation of order conditions using B-series, optimization of computational complexity per integration step and development of adaptive integration strategies. Performance of exponential integrators will be evaluated using a suite of test problems and comparing them with standard methods.

Last modified: Mon Nov 24 13:14:36 EST 2008