Operator splitting for the KdV equation

Helge Holden; Kenneth H. Karlsen; Nils Henrik Risebro; Terence Tao

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arXiv · 0906.4902

Operator splitting for the KdV equation

Helge Holden·Kenneth H. Karlsen·Nils Henrik Risebro·Terence Tao

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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.

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Helge Holden, Kenneth H. Karlsen, Nils Henrik Risebro, Terence Tao. 2009-06-26. Operator splitting for the KdV equation. https://arxiv.org/abs/0906.4902

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