Luis Lehner et al 2004 Class. Quantum Grav. 21 5819 doi:10.1088/0264-9381/21/24/009
Luis Lehner1, David Neilsen1,2, Oscar Reula3 and Manuel Tiglio1,4,5
Show affiliationsThe energy method can be used to identify well-posed initial boundary value problems for quasi-linear, symmetric hyperbolic partial differential equations with maximally dissipative boundary conditions. A similar analysis of the discrete system can be used to construct stable finite difference equations for these problems at the linear level. In this paper we apply these techniques to some test problems commonly used in numerical relativity and observe that while we obtain convergent schemes, fast growing modes, or 'artificial instabilities', contaminate the solution. We find that these growing modes can partially arise from the lack of a Leibnitz rule for discrete derivatives and discuss ways to limit this spurious growth.
02.60.Lj Ordinary and partial differential equations; boundary value problems
65M12 Stability and convergence of numerical methods
83C27 Lattice gravity, Regge calculus and other discrete methods
Issue 24 (21 December 2004)
Received 29 July 2004, in final form 19 October 2004
Published 25 November 2004
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