Operator splitting for the KdV equation

Details Operator splitting for the KdV equation Operator splitting for the KdV equation

2009-06-26

arxiv.org/abs/0906.4902v1

Mathematics

Analysis of PDEs

Scientific paper

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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