Non-existence of generalized splitting methods with positive coefficients of order higher than four
arXiv:1905.054926 citations
Originality Incremental advance
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Establishes a fundamental theoretical limit for numerical integration methods used in differential equations.
The paper proves that generalized exponential splitting methods with real coefficients cannot exceed order four, extending the known restriction from order two for classical methods.
We prove that generalized exponential splitting methods making explicit use of commutators of the vector fields are limited to order four when only real coefficients are admitted. This generalizes the restriction to order two for classical splitting methods with only positive coefficients.