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首页> 外文期刊>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
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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

机译：空间二阶，时间双曲系统的一阶有限差分方法和线性位移波方程作为数值相对论中的模型问题

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摘要

Motivated by the problem of solving the Einstein equations, we discuss high order finite difference discretizations of first order in time, second order in space hyperbolic systems. Particular attention is paid to the case when first order derivatives that can be identified with advection terms are approximated with non-centered finite difference operators. We first derive general properties of these discrete operators, then we extend a known result on numerical stability for such systems to general order of accuracy. As an application we analyze the shifted wave equation, including the behavior of the numerical phase and group speeds at different orders of approximations. Special attention is paid to when the use of off-centered schemes improves the accuracy over the centered schemes.
机译：出于解决爱因斯坦方程的问题，我们讨论了空间双曲系统中一阶，二阶时间的高阶有限差分离散化。特别注意以下情况：使用对中有限差分算子对可以用对流项识别的一阶导数进行近似。我们首先得出这些离散算子的一般性质，然后将此类系统的数值稳定性的已知结果扩展到一般精度。作为应用程序，我们分析了位移波方程，包括数值相位的行为和不同近似阶数下的组速度。与偏心方案相比，偏心方案的使用可提高准确性时要特别注意。

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