A splitting approach for the Kadomtsev--Petviashvili equation
arXiv:1407.8154 · doi:10.1016/j.jcp.2015.07.024
Abstract
We consider a splitting approach for the Kadomtsev--Petviashvili equation with periodic boundary conditions and show that the necessary interpolation procedure can be efficiently implemented. The error made by this numerical scheme is compared to exponential integrators which have been shown in Klein and Roidot (SIAM J. Sci. Comput., 2011) to perform best for stiff solutions of the Kadomtsev--Petviashvili equation. Since many classic high order splitting methods do not perform well, we propose a stable extrapolation method in order to construct an efficient numerical scheme of order four. In addition, the conservation properties and the possibility of order reduction for certain initial values for the numerical schemes under consideration is investigated.
References in corpus (1)
Cited by in corpus (11)
- High performance computing aspects of a dimension independent semi-Lagrangian discontinuous Galerkin code
- On the performance of exponential integrators for problems in magnetohydrodynamics
- Exponential methods for solving hyperbolic problems with application to kinetic equations
- An exponential integrator for the drift-kinetic model
- Exponential Integrators for Resistive Magnetohydrodynamics: Matrix-free Leja Interpolation and Efficient Adaptive Time Stepping
- A comparison of boundary correction methods for Strang splitting
- Nonlinear ion acoustic waves scattered by vortexes
- A split step Fourier/discontinuous Galerkin scheme for the Kadomtsev--Petviashvili equation
- On the error propagation of semi-Lagrange and Fourier methods for advection problems
- An exponential-type integrator for the KdV equation
- A pseudo-spectral splitting method for linear dispersive problems with transparent boundary conditions