Operator splitting is used in many applications. By decomposing the operator into a sum, each term can be integrated separately, either exactly or by an efficient numerical method, and an approximation to the original problem is obtained by composition. When the splitting represents the stiff and nonstiff parts of ODE, it is known that one may observe order reduction similar to the B-convergence theory for Runge-Kutta methods. This phenomenon can not be explained by the classical error analysis. Based on the Taylor series expansions of the exact solution and the splitting method solution the classical error analysis fails for large time steps.

We propose a framework to analyze the order reduction of the splitting methods. Several types of splitting methods are examined for linear ODE systems and linear PDEs (which can be viewed as ODEs formulated in abstract spaces). The results are supported by numerical experiments.

MINISIMPOSIUM SESSION: 12. Lie Group methods