High order finite difference approximations are derived for a one-dimensional model of the shifted wave equation written in second-order form. Thedomain is discretized using fully compatible summation by parts operato...High order finite difference approximations are derived for a one-dimensional model of the shifted wave equation written in second-order form. Thedomain is discretized using fully compatible summation by parts operators and theboundary conditions are imposed using a penalty method, leading to fully explicittime integration. This discretization yields a strictly stable and efficient scheme. Theanalysis is verified by numerical simulations in one-dimension. The present study isthe first step towards a strictly stable simulation of the second-order formulation ofEinstein’s equations in three spatial dimensions.展开更多
文摘High order finite difference approximations are derived for a one-dimensional model of the shifted wave equation written in second-order form. Thedomain is discretized using fully compatible summation by parts operators and theboundary conditions are imposed using a penalty method, leading to fully explicittime integration. This discretization yields a strictly stable and efficient scheme. Theanalysis is verified by numerical simulations in one-dimension. The present study isthe first step towards a strictly stable simulation of the second-order formulation ofEinstein’s equations in three spatial dimensions.
