Author:
Einkemmer L.,Ostermann A.,Residori M.
Abstract
AbstractThe 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.
Funder
University of Innsbruck and Medical University of Innsbruck
Publisher
Springer Science and Business Media LLC
Subject
Applied Mathematics,Computational Mathematics
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