TY - JOUR
T1 - Stable and Accurate Second-Order Formulation of the Shifted Wave Equation
JO - Communications in Computational Physics
VL - 1
SP - 103
EP - 137
PY - 2010
DA - 2010/07
SN - 7
DO - http://doi.org/10.4208/cicp.2009.08.135
UR - https://global-sci.org/intro/article_detail/cicp/7621.html
KW - 
AB - <p style="text-align: justify;">High order finite difference approximations are derived for a one-dimensional
model of the shifted wave equation written in second-order form. The
domain is discretized using fully compatible summation by parts operators and the
boundary conditions are imposed using a penalty method, leading to fully explicit
time integration. This discretization yields a strictly stable and efficient scheme. The
analysis is verified by numerical simulations in one-dimension. The present study is
the first step towards a strictly stable simulation of the second-order formulation of
Einstein&#39;s equations in three spatial dimensions.</p>