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Stable and Accurate Second-Order Formulation of the Shifted Wave Equation

Stable and Accurate Second-Order Formulation of the Shifted Wave Equation
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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

Keywords:   

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