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 766 time(s).
DoubleIntegralRK.pdf (219.12 KiB) downloaded 460 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 587 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 724 time(s).
GaussLegendreQuadrature.pdf (160.77 KiB) downloaded 413 time(s).

Best regards.
Alvaro.

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

Yes.

DoubleIntegralSteelCat.sm (47.08 KiB) downloaded 695 time(s).
DoubleIntegralSteelCat.pdf (105.49 KiB) downloaded 358 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 615 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 615 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 689 time(s).
DoubleIntegralJean.pdf (45.11 KiB) downloaded 398 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