Exponential splitting for unbounded operators
Författare
Summary, in English
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 then 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.
abstract framework of (semi)groups. The convergence analysis also includes generalizations to splittings consisting of more then 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.
Publiceringsår
2009
Språk
Engelska
Sidor
1485-1496
Publikation/Tidskrift/Serie
Mathematics of Computation
Volym
78
Issue
267
Dokumenttyp
Artikel i tidskrift
Förlag
American Mathematical Society (AMS)
Ämne
- Electrical Engineering, Electronic Engineering, Information Engineering
Nyckelord
- splitting schemes
- convergence
- nonstiff order
- Schrödinger equation
- unbounded operators
- Exponential splitting
Status
Published
ISBN/ISSN/Övrigt
- ISSN: 1088-6842