Year: 2019
Type: preprint
Abstract: This paper provides an algebraic framework for the generation of order conditions for the construction of exponential integrators like splitting and Magnus-type methods for the numerical solution of evolution equations. The generation of order conditions is based on an analysis of the structure of the leading local error term of such an integrator, and on a new algorithm for the computation of coefficients of words in expressions involving exponentials. As an application a new 8th order commutator-free Magnus-type integrator involving only 8 exponentials is derived.
Source: arXiv (Cornell University)
Author: Hofstätter, Harald
Institution: University of Vienna
Language: English
Subfield: Numerical Analysis
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Funder: Austrian Science Fund
OpenAlex ID: W2915458641