Preprint 2009-038
Operator splitting for the KdV equation
Helge Holden, Kenneth H. Karlsen, Nils Henrik Risebro and Terence Tao
Abstract: We provide a new analytical approach to operator splitting for equations of the type ut=Au+B(u) where A is a linear operator and B is quadratic. A particular example is the Korteweg–de Vries (KdV) equation ut−uux+uxxx=0. We show that the Godunov and Strang splitting methods converge with the expected rates if the initial data are sufficiently regular.