## Operator splitting for partial differential equations with Burgers nonlinearity

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- by Helge Holden, Christian Lubich and Nils Henrik Risebro PDF
- Math. Comp.
**82**(2013), 173-185 Request permission

## Abstract:

We provide a new analytical approach to operator splitting for equations of the type $u_t=Au+u u_x$ where $A$ is a linear differential operator such that the equation is well-posed. Particular examples include the viscous Burgers equation, the Korteweg–de Vries (KdV) equation, the Benney–Lin equation, and the Kawahara equation. We show that the Strang splitting method converges with the expected rate if the initial data are sufficiently regular. In particular, for the KdV equation we obtain second-order convergence in $H^r$ for initial data in $H^{r+5}$ with arbitrary $r\ge 1$.## 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
**Christian Lubich**- Affiliation: Mathematisches Institut, Universität Tübingen, Auf der Morgenstelle 10, D–72076 Tübingen, Germany
- MR Author ID: 116445
- Email: lubich@na.uni-tubingen.de
**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
- Received by editor(s): February 8, 2011
- Published electronically: June 12, 2012
- Additional Notes: This work was supported in part by the Research Council of Norway.
- © Copyright 2012
American Mathematical Society

The copyright for this article reverts to public domain 28 years after publication. - Journal: Math. Comp.
**82**(2013), 173-185 - MSC (2010): Primary 35Q53; Secondary 65M12, 65M15
- DOI: https://doi.org/10.1090/S0025-5718-2012-02624-X
- MathSciNet review: 2983020