A custom sinc GUI
This page is under construction; it illustrates one way of dealing
with the complications encountered in the approximation of singular
functions, here using results from sinc methods.
Using the resulting GUIThese above elements are combined, along with some other selection mechanisms, to enable some close-up viewing of singular functions. For example, the following shows the computed (N=18) solution along a horizontal slice near y=0.2:
This could (possibly) be done with other methods; but the interesting part is closer to the singularity at (0,0):
Now, it's not clear what the behavior is near the interesting region. But this is no problem; just use the array range sliders, and zoom in on the location graph:
Now the behavior near x=0 is clear. The gap between the left and right domain (orange and brown lines) is needed when approximating derivatives near singularities.