Setup of Order Conditions for Splitting Methods
Provides a practical computational tool for researchers working on splitting methods, but the approach is incremental as it automates existing theory.
The paper implements a computer algebra approach (in Maple 18) for setting up order conditions for operator splitting methods, building on prior theoretical work. It describes a parallel version of the code.
This article is based on earlier papers where an approach based on Taylor expansion and the structure of its leading term as an element of a free Lie algebra was described for the setup of a system of order conditions for operator splitting methods. Along with a brief review of these materials and some theoretical background, we discuss the implementation of the ideas from these papers in computer algebra, in particular using Maple 18. A parallel version of such a code is described.