Order conditions for exponential integrators
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Publication:6314825
arXiv1902.11256MaRDI QIDQ6314825
Publication date: 28 February 2019
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.
Has companion code repository: https://github.com/HaraldHofstaetter/Expocon.mpl
Symbolic computation and algebraic computation (68W30) Combinatorics on words (68R15) Numerical methods for initial value problems involving ordinary differential equations (65L05) Numerical solutions to abstract evolution equations (65J08)
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