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Motivated by the problem of solving the Einstein equations, we discuss highorder finite difference discretizations of first order in time, second order inspace hyperbolic systems.Particular attention is paid to the case when firstorder derivatives that can be identified with advection terms are approximatedwith non-centered finite difference operators.We first derive generalproperties of these discrete operators, then we extend a known result onnumerical stability for such systems to general order of accuracy.As anapplication we analyze the shifted wave equation, including the behavior of thenumerical phase and group speeds at different orders of approximations. Specialattention is paid to when the use of off-centered schemes improves the accuracyover the centered schemes.

journal of computational physics

Finite Difference Methods for Second Order in Space, First Order in Time  Hyperbolic Systems and the Linear Shifted Wave Equation as a Model Problem in  Numerical Relativity