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zhk

00:25

@xzczd I want to integrate w w.r.t. x and y and want to keep one parameter for plotting.

Module[{y},
NDSolveValue[{(1 + 0.1*I)*(D[w[y], {y, 2}]) - (Ha^2 + 1*I)*w[y] +
Ha*5 == 0, w[1 + 0.1 Sin[0.1 x]] == 0, w[-1 - 0.1 Sin[0.1 x]] == 0},
w, {y, -1 - 0.1 Sin[0.1 x], 1 + 0.1 Sin[0.1 x]}]]
Any suggestion?
here lambda is 1

2 hours later…

xzczd

02:44

@zhk Using NIntegrate directly should be enough, I think. To speed up the calculation, you may need "SymbolicProcessing" -> 0: mathematica.stackexchange.com/a/118180/1871

Since the variation of w[x,y] is "gentle" you can also consider building a InterpolatingFunction with Interpolation first.

zhk

@xzczd I tried this
sol[x_, Ha_] :=
Module[{y},
NDSolveValue[{(1 + 0.1*I)*(D[w[y], {y, 2}]) - (Ha^2 + 1*I)*w[y] +
Ha*5 == 0, w[1 + 0.1 Sin[0.1 x]] == 0, w[-1 - 0.1 Sin[0.1 x]] == 0},
w, {y, -1 - 0.1 Sin[0.1 x], 1 + 0.1 Sin[0.1 x]}]]
NIntegrate[
sol[x, 0.5][y], {x, 0, 1}, {y, -1 - 0.1 Sin[0.1 x],
1 + 0.1 Sin[0.1 x]}]

but it gives a warrning
NDSolveValue::ndsv: Cannot find starting value for the variable w.

xzczd

03:41

@zhk That's merely a warning, if you don't want it, just use:

Clear@sol
sol[x_?NumericQ, Ha_] :=
 Module[{y},
  NDSolveValue[{(1 + 0.1*I)*(D[w[y], {y, 2}]) - (Ha^2 + 1*I)*w[y] + Ha*5 == 0,
    w[1 + 0.1 Sin[0.1 x]] == 0, w[-1 - 0.1 Sin[0.1 x]] == 0},
   w, {y, -1 - 0.1 Sin[0.1 x], 1 + 0.1 Sin[0.1 x]}]]

zhk

@xzczd but when I do this,
wm[Ha_] :=
NIntegrate[
sol[x, Ha][y], {x, 0, 1}, {y, -1 - 0.1 Sin[0.1 x],
1 + 0.1 Sin[0.1 x]}]
dat = Partition[Flatten[Table[{Ha, Re@wm[Ha]}, {Ha, 0, 1, 0.5}]], 3]

it just give errors no output

@ Is there any other elegant way to do this? its very time consuming. I also used ur suggestion.

it took long but no output
Method -> {Automatic, "SymbolicProcessing" -> 0}

with this ?NumericQ, the process take less time but there is no output

zhk

04:39

@xzczd For some reason which i dont know, there was a problem with my notebook.
After starting a new one,
Clear@sol
sol[x_?NumericQ, Ha_] :=
Module[{y},
NDSolveValue[{(1 + 0.1*I)*(D[w[y], {y, 2}]) - (Ha^2 + 1*I)*w[y] +
Ha*5 == 0, w[1 + 0.1 Sin[0.1 x]] == 0,
w[-1 - 0.1 Sin[0.1 x]] == 0},
w, {y, -1 - 0.1 Sin[0.1 x], 1 + 0.1 Sin[0.1 x]}]]
NIntegrate[
sol[x, 0.5][y], {x, 0, 1}, {y, -1 - 0.1 Sin[0.1 x],
1 + 0.1 Sin[0.1 x]}]
1.27018 - 0.579235 I
it produces a result quickly, but when i do this,

Table[NIntegrate[

zhk

05:04

@xzczd The problem was with Ha=0, if we take something close to zero then its working fine. Thx dear

2 hours later…

xzczd

07:33

@zhk Also, don't forget the sol[x_?NumericQ, Ha_] := sol[x, Ha] = trick

zhk

08:33

@xzczd OK I will not. thx. Any hint for the interpolating function w[x,y,Ha]?

@xzczd here is the final form, its working fine just a little slow
https://www.dropbox.com/s/9zy5tzityvbhagk/mv.nb?dl=0

hftf

09:17

Is it just me, or does anyone think it is kind of weird for someone to take a new technique from an answer, and then use it to write new answers to several old questions that are essentially duplicates, instead of to just flag those questions as duplicates?

I didn't flag the duplicates myself because I assumed someone with 3 magnitudes more rep than me knows what they are doing, but I guess I'm the only one who wants to centralize identical resources in one place.

J. M.

09:37

@hftf Centralization is perfectly fine. As for deciding whether posts are dupes or not, that's why it takes a few (non-mod) people to close. At least you've set up a signpost.

(Also, since you've linked to them, they will now show up in the sidebar, too.)

hftf

Thanks. I think they might also have first appeared in the sidebar after I commented on the linked questions, but before I edited the post with the links.

xzczd

09:51

@zhk The GFW seems to be a bit… tight at the moment so I can't access dropbox now… The interpolation is quite straightforward, just combine Table and ListInterpolation. Remember this needs to be done in a regular region i.e. you need to use a Table similar to the one mentioned here.

hftf

@b3m2a1 I enjoyed your blog posts investigating the stack exchange data.

However I might interpret "there are more higher voted questions late at night" as due to "fewer questions are asked during that time, and so they tend to stay up on the front page longer, exposing more people to see it and vote on it". I also wanted to recommend adding axis labels and other such labels to your plots, since it was tough to skim them quickly.

I thought it was a little strange to look for the correlation "peaks in total questions over time vs. new versions of Mathematica" using "functions introduced in specific versions" as a proxy for "questions pertaining to a specific version" - you could easily plot "questions containing the new function's name" using the same dataset instead, right?

2 hours later…

PlatoManiac

11:58

@b3m2a1 Any chance you know why `URLDispatcher` not allowing the `APIFunction` to access the body of a HTTP request. I posted a question on that. Thought of asking you here as you have worked with hosting pages and web services.

4 hours later…

Alucard