Type: Article
Publication Date: 2010-12-29
Citations: 79
DOI: https://doi.org/10.1090/s0025-5718-2010-02402-0
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.