Stable and Accurate Second-Order Formulation of the Shifted Wave Equation
Year: 2010
Communications in Computational Physics, Vol. 7 (2010), Iss. 1 : pp. 103–137
Abstract
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's equations in three spatial dimensions.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/cicp.2009.08.135
Communications in Computational Physics, Vol. 7 (2010), Iss. 1 : pp. 103–137
Published online: 2010-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 35
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