Order conditions for exponential integrators

2019/02/28 by Harald Hofstätter, Hofstätter, Harald
Computer Science · Engineering · Mathematics · #65J08 #65L05 #68R15 #68W30 #Advanced Numerical Methods in Computational Mathematics #FOS: Mathematics #Modeling and Simulation Systems #Numerical Analysis (math.NA) #Numerical methods for differential equations

paper · pdf · doi:10.48550/arxiv.1902.11256

openalex publication_date 2019/02/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

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