A review of error analysis for splitting methods and exponential integrators

A review of error analysis for splitting methods and exponential integrators by Bård Skaflestad preprint numerics no. 9/2005 norwegian university of science and technology trondheim, norway We briefly review splitting methods for differential equations and the error analysis of such schemes available in the literature, and present several types of splitting methods. Some of the mathematical tools needed in the analysis are listed for reference. Progressing from splitting methods based on exact flow maps through methods using numerical flow map approximations, we also list some of the splitting methods in common use for time integration of in-compressible fluid flow problems. We finally present the class of " exponential integrators " in some detail and give an outline of the concept of stiff order conditions recently introduced by Hochbruck and Ostermann to analyse exponential integrators applied to semi-linear parabolic problems.