User: bmundim Date: 2012/03/13 12:07 AM

Modified: / ET.tex

Log: (2,2) \psi_4 phase and amplitude convergence studies.

File Changes:

Directory: / ============

File [modified]: ET.tex Delta lines: +3 -2 =================================================================== --- ET.tex 2012-03-13 04:46:44 UTC (rev 296) +++ ET.tex 2012-03-13 05:07:41 UTC (rev 297) @@ -2714,10 +2714,11 @@ In order to evaluate the convergence of the numerical solution, we ran five simulations with different resolutions, and focus our analysis on the convergence -of the phase and amplitude of the Weyl scalar $\Psi_4$. +of the phase and amplitude of the Weyl scalar $(2,2)$ mode, +$\Psi_4^{(2,2)}$.

Here, we consider the phase $\varphi(t)$ and -the amplitude $A(t)$ of the Weyl scalar $\Psi_4$ at +the amplitude $A(t)$ of the Weyl scalar $(2,2)$ mode $\Psi_4^{(2,2)}$ at $R_{\rm obs}=60\mathrm{M}$. In order to take differences between the numerical values at two different grid resolutions, we use an $8$-th order accurate Lagrange operator to interpolate the higher-accuracy finite difference solution