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Efficient integration of large stiff systems of ODEs with exponential propagation iterative (EPI) methods. (English) Zbl 1089.65063
Summary: A new class of exponential propagation techniques which we call exponential propagation iterative (EPI) methods is introduced. 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 ordinary differential equations (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.

65L05 Numerical methods for initial value problems involving ordinary differential equations
34A34 Nonlinear ordinary differential equations and systems
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