An exponential-type integrator for the KdV equation

Abstract

We introduce an exponential-type time-integrator for the KdV equation and prove its first-order convergence in $H^1$ for initial data in $H^3$. Furthermore, we outline the generalization of the presented technique to a second-order method.

References in corpus (1)

• A splitting approach for the Kadomtsev--Petviashvili equation

Cited by in corpus (1)

• Uniformly accurate exponential-type integrators for klein-gordon equations with asymptotic convergence to classical splitting schemes in the nonlinear schroedinger limit