Operator splitting for the KdV equation
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- by Helge Holden, Kenneth H. Karlsen, Nils Henrik Risebro and Terence Tao PDF
- Math. Comp. 80 (2011), 821-846 Request permission
Abstract:
We provide a new analytical approach to operator splitting for equations of the type $u_t=Au+B(u)$, where $A$ is a linear operator and $B$ is quadratic. A particular example is the Korteweg–de Vries (KdV) equation $u_t-u u_x+u_{xxx}=0$. We show that the Godunov and Strang splitting methods converge with the expected rates if the initial data are sufficiently regular.References
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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
- MR Author ID: 361755
- ORCID: 0000-0002-0140-7641
- Email: tao@math.ucla.edu
- 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.
- © Copyright 2010
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - 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
- MathSciNet review: 2772097