@Article{CiCP-7-1, author = {}, title = {Stable and Accurate Second-Order Formulation of the Shifted Wave Equation}, journal = {Communications in Computational Physics}, year = {2010}, volume = {7}, number = {1}, pages = {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.

}, issn = {1991-7120}, doi = {https://doi.org/10.4208/cicp.2009.08.135}, url = {https://global-sci.com/article/80970/stable-and-accurate-second-order-formulation-of-the-shifted-wave-equation} }