Exponential splitting for unbounded operators

Hansen, Eskil; Ostermann, Alexander

doi:10.1090/S0025-5718-09-02213-3

Exponential splitting for unbounded operators
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by Eskil Hansen and Alexander Ostermann;

Math. Comp. 78 (2009), 1485-1496

DOI: https://doi.org/10.1090/S0025-5718-09-02213-3

Published electronically: January 22, 2009

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Abstract:

We present a convergence analysis for exponential splitting methods applied to linear evolution equations. Our main result states that the classical order of the splitting method is retained in a setting of unbounded operators, without requiring any additional order condition. This is achieved by basing the analysis on the abstract framework of (semi)groups. The convergence analysis also includes generalizations to splittings consisting of more than two operators, and to variable time steps. We conclude by illustrating that the abstract results are applicable in the context of the Schrödinger equation with an external magnetic field or with an unbounded potential.

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