Double Integration using ode solvers

#1 Posted: 6/4/2020 1:40:08 AM

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Hi. This worksheet shows how to use an ode solver for evaluating a double integral over the region between two functions.

DoubleIntegralRK.sm (42.67 KiB) downloaded 803 time(s).
DoubleIntegralRK.pdf (219.12 KiB) downloaded 479 time(s).

Best regards.
Alvaro.

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frapuano 6/4/2020 4:03:00 AM, sergio 6/4/2020 4:42:00 AM

#2 Posted: 6/7/2020 1:21:46 PM

SteelCat

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Thanks Alvaro for your example.

Can the change of variable be put in the procedure definition?

Physics is like sex. Sure, it may give some practical results, but that’s not why we do it. (R. Feynman)

#3 Posted: 6/7/2020 7:50:25 PM

Jean Giraud

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Wrote
Can the change of variable be put in the procedure definition,?

Like this: yes, just opposite plot.

Double Switch [x, L].sm (6.33 KiB) downloaded 616 time(s).

#4 Posted: 6/17/2020 8:21:22 PM

Alvaro Diaz Falconi

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Hi. This is the double integral using Gauss Legendre quadrature.

GaussLegendreQuadrature.sm (60.58 KiB) downloaded 761 time(s).
GaussLegendreQuadrature.pdf (160.77 KiB) downloaded 431 time(s).

Best regards.
Alvaro.

Wrote
...
Can the change of variable be put in the procedure definition?

Yes.

DoubleIntegralSteelCat.sm (47.08 KiB) downloaded 724 time(s).
DoubleIntegralSteelCat.pdf (105.49 KiB) downloaded 376 time(s).

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sergio 6/18/2020 5:14:00 AM, frapuano 6/18/2020 7:33:00 AM

#5 Posted: 6/18/2020 11:26:19 AM

Jean Giraud

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Keisan has longer Legendre than 64, but couldn't copy/paste ?
From other source: 63, 64.

Integrate Legendre [ Wr 24 ].sm (28.98 KiB) downloaded 640 time(s).

#6 Posted: 6/18/2020 9:35:42 PM

Alvaro Diaz Falconi

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Keisan has longer Legendre than 64, but couldn't copy/paste ?
From other source: 63, 64.

Integrate Legendre [ Wr 24 ].sm (28.98 KiB) downloaded 640 time(s).

Hi Jean. Yes, can copy and paste. Do that first into excel, and from there to the small SMathMatrixEditor and finally paste in SMath.

In the attached Laguerre and Legendre coeffs for the Gauss method.

DoubleIntegralJean.sm (25.63 KiB) downloaded 718 time(s).
DoubleIntegralJean.pdf (45.11 KiB) downloaded 412 time(s).

Best regards.
Alvaro

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sergio 6/19/2020 5:41:00 AM, frapuano 6/19/2020 9:34:00 AM

#7 Posted: 6/20/2020 7:39:28 AM

Jean Giraud

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Hi Jean. Yes, can copy and paste.

Thanks, Amigo !

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Double Integration using ode solvers - Messages