Symmetric-conjugate splitting methods for linear unitary problems

We analyze the preservation properties of a family of reversible splitting methods when they are applied to the numerical time integration of linear differential equations defined in the unitary group. The schemes involve complex coefficients and are conjugated to unitary transformations for suffici...

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Bibliographic Details
Published in:BIT 2023-12, Vol.63 (4), Article 58
Main Authors: Bernier, J., Blanes, S., Casas, F., Escorihuela-Tomàs, A.
Format: Article
Language:English
Subjects:
Computational Mathematics and Numerical Analysis
Differential equations
Mathematics
Mathematics and Statistics
Numeric Computing
Numerical Analysis
Schrodinger equation
Splitting
Time integration
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Summary:We analyze the preservation properties of a family of reversible splitting methods when they are applied to the numerical time integration of linear differential equations defined in the unitary group. The schemes involve complex coefficients and are conjugated to unitary transformations for sufficiently small values of the time step-size. New and efficient methods up to order six are constructed and tested on the linear Schrödinger equation.
ISSN:0006-3835
1572-9125
DOI:10.1007/s10543-023-00998-4