On the Numerical Stability of the Einstein Equations
| dc.creator | Miller, Mark | |
| dc.date | 2000-08-08 | |
| dc.date.accessioned | 2026-07-07T03:25:11Z | |
| dc.date.available | 2026-07-07T03:25:11Z | |
| dc.description | We perform a von Neumann stability analysis on a common discretization of the Einstein equations. The analysis is performed on two formulations of the Einstein equations, namely, the standard ADM formulation and the conformal-traceless (CT) formulation. The eigenvalues of the amplification matrix are computed for flat space as well as for a highly nonlinear plane wave exact solution. We find that for the flat space initial data, the condition for stability is simply $\frac {Δt}{Δz} \leq 1$. However, a von Neumann analysis for highly nonlinear plane wave initial data shows that the standard ADM formulation is unconditionally unstable, while the conformal-traceless (CT) formulation is stable for $0.25 \leq \frac {Δt}{Δz} < 1$. | |
| dc.description | 14 pages, 9 figures, submitted to Phys. Rev. D | |
| dc.identifier | https://arxiv.org/abs/gr-qc/0008017 | |
| dc.identifier | http://arxiv.org/abs/gr-qc/0008017 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/33612 | |
| dc.subject | General Relativity and Quantum Cosmology | |
| dc.title | On the Numerical Stability of the Einstein Equations | |
| dc.type | text |