Operator splitting for the KdV equation

Authors:
Helge Holden, Kenneth H. Karlsen, Nils Henrik Risebro and Terence Tao

Journal:
Math. Comp. **80** (2011), 821-846

MSC (2010):
Primary 35Q53; Secondary 65M12, 65M15

DOI:
https://doi.org/10.1090/S0025-5718-2010-02402-0

Published electronically:
September 17, 2010

MathSciNet review:
2772097

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Abstract | References | Similar Articles | Additional Information

Abstract: We provide a new analytical approach to operator splitting for equations of the type , where is a linear operator and is quadratic. A particular example is the Korteweg-de Vries (KdV) equation . We show that the Godunov and Strang splitting methods converge with the expected rates if the initial data are sufficiently regular.

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Additional Information

**Helge Holden**

Affiliation:
Department of Mathematical Sciences, Norwegian University of Science and Technology, NO–7491 Trondheim, Norway and Centre of Mathematics for Applications, University of Oslo, P.O. Box 1053, Blindern, NO–0316 Oslo, Norway

Email:
holden@math.ntnu.no

**Kenneth H. Karlsen**

Affiliation:
Centre of Mathematics for Applications, University of Oslo, P.O. Box 1053, Blindern, NO–0316 Oslo, Norway

Email:
kennethk@math.uio.no

**Nils Henrik Risebro**

Affiliation:
Centre of Mathematics for Applications, University of Oslo, P.O. Box 1053, Blindern, NO–0316 Oslo, Norway

Email:
nilshr@math.uio.no

**Terence Tao**

Affiliation:
Department of Mathematics, University of California at Los Angeles, Los Angeles, California 90095-1555

Email:
tao@math.ucla.edu

DOI:
https://doi.org/10.1090/S0025-5718-2010-02402-0

Keywords:
KdV equation,
operator splitting

Received by editor(s):
June 6, 2009

Received by editor(s) in revised form:
December 9, 2009

Published electronically:
September 17, 2010

Additional Notes:
Supported in part by the Research Council of Norway. This paper was written as part of the international research program on Nonlinear Partial Differential Equations at the Centre for Advanced Study at the Norwegian Academy of Science and Letters in Oslo during the academic year 2008–09. The fourth author is supported by a grant from the MacArthur Foundation, the NSF Waterman award, and NSF grant DMS-0649473.

Article copyright:
© Copyright 2010
American Mathematical Society

The copyright for this article reverts to public domain 28 years after publication.