Setup of Order Conditions for Splitting Methods

TL;DR

This paper reviews and implements a Lie algebra-based approach to derive order conditions for splitting methods, providing computational tools and parallel algorithms for efficient symbolic calculations.

Contribution

It introduces a computer algebra implementation, including a parallel version, of the Lie algebra approach for setting up order conditions in splitting methods.

Findings

Successful implementation in Maple 18

Parallel algorithm enhances computational efficiency

Provides a practical tool for researchers in numerical analysis

Abstract

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.