A pseudo-spectral Strang splitting method for linear dispersive problems with transparent boundary conditions
Abstract
The present work proposes a second-order time splitting scheme for a linear dispersive equation with a variable advection coefficient subject to transparent boundary conditions. For its spatial discretization, a dual Petrov--Galerkin method is considered which gives spectral accuracy. The main difficulty in constructing a second-order splitting scheme in such a situation lies in the compatibility condition at the boundaries of the sub-problems. In particular, the presence of an inflow boundary condition in the advection part results in order reduction. To overcome this issue a modified Strang splitting scheme is introduced that retains second-order accuracy. For this numerical scheme a stability analysis is conducted. In addition, numerical results are shown to support the theoretical derivations.
Cite
@article{arxiv.2006.05170,
title = {A pseudo-spectral Strang splitting method for linear dispersive problems with transparent boundary conditions},
author = {Lukas Einkemmer and Alexander Ostermann and Mirko Residori},
journal= {arXiv preprint arXiv:2006.05170},
year = {2021}
}