A Fully Pseudospectral Scheme for Solving Singular Hyperbolic Equations

Details A Fully Pseudospectral Scheme for Solving Singular Hyperbolic Equations A Fully Pseudospectral Scheme for Solving Singular Hyperbolic Equations

2008-01-09

arxiv.org/abs/0801.1455v2

J.Hyperbol.Diff.Equat.6:161,2009

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

24 pages, 12 figures

Scientific paper

10.1142/S0219891609001769

With the example of the spherically symmetric scalar wave equation on Minkowski space-time we demonstrate that a fully pseudospectral scheme (i.e. spectral with respect to both spatial and time directions) can be applied for solving hyperbolic equations. The calculations are carried out within the framework of conformally compactified space-times. In our formulation, the equation becomes singular at null infinity and yields regular boundary conditions there. In this manner it becomes possible to avoid "artificial" conditions at some numerical outer boundary at a finite distance. We obtain highly accurate numerical solutions possessing exponential spectral convergence, a feature known from solving elliptic PDEs with spectral methods. Our investigations are meant as a first step towards the goal of treating time evolution problems in General Relativity with spectral methods in space and time.

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