This plot shows the convergence ratio versus time of the g11 metric component obtained by taking the ratio of the norm of the error between the evolved hypersurface and the exact Novikov solution at two different grid resolutions. For our 65^3 and 33^3 runs we double the grid spacing and hence should obtain a ratio of 4.0 for our second order evolution scheme. Since the 65^3 grid updates twice as often compared to the 33^3 grid, the relativily large error at the horizon grid points is excised earlier, thus inflating the convergence ratio to values greater than 4.0. Over time, the error from the growing instabilities at the boundaries causes the convergence to fall well below 4.0, indicating a divergent solution.

A plot of the norm of the error versus time for the g11 cartesian metric component shows a nearly exponential growth of the error, indicating the numerical evolution scheme is unstable.