Commun. Comput. Phys., 7 (2010), pp. 103-137.


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

Ken Mattsson 1*, Florencia Parisi 2

1 Department of Information Technology, Uppsala University, P.O. Box 337, S-751 05 Uppsala, Sweden.
2 FaMAF, Universidad Nacional de Cordoba, Medina Allende S/N Ciudad Universitaria, 5000 Cordoba, Argentina.

Received 20 August 2008; Accepted (in revised version) 4 May 2009
Available online 16 July 2009
doi:10.4208/cicp.2009.08.135

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.

AMS subject classifications: 35L05, 35L20, 65N06, 65N12, 83C05

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Key words: High-order finite difference methods, wave equation, numerical stability, second derivatives, Einstein's equations.

*Corresponding author.
Email: ken.mattsson@it.uu.se (K. Mattsson), fparisi@famaf.unc.edu.ar (F. Parisi)
 

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