Operator splitting for dispersion-generalized Benjamin-Ono equations
arXiv:1801.051301.2
Originality Synthesis-oriented
AI Analysis
Provides rigorous convergence guarantees for operator splitting methods on a class of nonlinear dispersive equations, benefiting numerical analysts and computational scientists.
The authors prove first-order convergence in Sobolev space for Godunov splitting and second-order for Strang splitting applied to a class of nonlinear equations including KdV, Benjamin-Ono, and Burgers equations.
We consider the operator splitting for a class of nonlinear equation, which includes the KdV equation, the Benjamin-Ono equation, and the Burgers equation. We prove a first-order approxomation in $Δt$ in the Sobolev space for the Godunov splitting, and second-order approximation for the Strang splitting.