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Abstract
High order finite difference approximations are derived for a onedimensional 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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