Efficient integration of large stiff systems of ODEs with exponential propagation iterative (EPI) methods

A new class of exponential propagation techniques which we call exponential propagation iterative (EPI) methods is introduced in this paper. It is demonstrated how for large stiff systems these schemes provide an efficient alternative to standard integrators for computing solutions over long time intervals. The EPI methods are constructed by reformulating the integral form of a solution to a nonlinear autonomous system of ODEs as an expansion in terms of products between special functions of matrices and vectors that can be efficiently approximated using Krylov subspace projections. The methodology for constructing EPI schemes is presented and their performance is illustrated using numerical examples and comparisons with standard explicit and implicit integrators. The history of the exponential propagation type integrators and their connection with EPI schemes are also discussed.