Strum, without knowing the exact 9-point stencil you used I tried to replicate the plot you produced (in Matlab I assume?). Apparently, there is no standard for the 9-point kernel although there is some consensus on the 5-point kernel. Different formulations of the finite difference formulae will yield differing kernels. So when I use a 9 point kernel, I obtain the following for the same domain and [itex]\Delta x = \Delta y = h = 0.1[/itex]I cant seem to figure out how to edit the post :/. Here is a pic of the error I gethttp://tinypic.com/r/25tjkm1/9
It seems like I get a very small [itex]|\epsilon|^2[/itex]By the way, the reason I am insisting on using convolution is purely for computational reasons: it can be done in hardware (ie. GPU). It seems like we both have comparable rates. The 5-point stencil yields the following result:
Notice that there are some artefacts that appear about one of the "color rings" in the last errror plot. Were you using another method other than convolution?