Operator splitting for the KdV equation
About
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.
Helge Holden, Kenneth H. Karlsen, Nils Henrik Risebro, Terence Tao• 2009
Related benchmarks
| Task | Dataset | Result | Rank | |
|---|---|---|---|---|
| Solving Quadratic Nonlinear Schrödinger Equation | Quadratic Nonlinear Schrödinger Equation (T=1.0, N=1024, γ=0.5) | L2 Error0.118 | 21 | |
| Numerical Integration | Cubic NLS T=1.0, N=1024, γ=0.5 | L2 Error0.0788 | 16 |
Showing 2 of 2 rows