Cauchy Integral Experiment

[mike3]

Ok, Mik. Thank you for the pics.
They confirm my suspections about the ends of the interval: a lot of variation there.

Yeah. It's the endpoints that are apparently causing all the trouble Which I find extremely peculiar, esp. the circle contour, since mathematically that _should_ work.

Does your iteration keep the function which is just constant L everywhere?
Could you check this?

OK, now that's weird. A massive disturbance develops in the initially flat line (line pair, actually, due to there being both real and imag parts) when I do that:

   

(one iteration of OneIteration(v, 10.0) on 209 nodes all set to L)

As you can see there's that whacko curve and that shouldn't be there. The pass should hardly change the array if change it at all. There's something very very bad happening near the left endpoint... I'm betting this is the source of the problem... (note that I don't update the two endpoints themselves as they lie right on the contour, remember the semicircle thing was failing... but maybe it wasn't, maybe there's something wrong with my integration routine, I'll have to check it some more)

Does your iteration keep the function which is precise tetrational at the first?
Could you check this?

I suppose I could, but given the problem I just mentioned above, I think it'd be best to address that first.

As for the residual, the single value at zero does not brung much information.
You should plot the residual along the imaginary axis.

And what's "step"? Number of nodes?

I mean the distance between nodes. As I understand, your nodes are equidistant.
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So if we hold A constant then that would translate to increasing the node number?