Double Integration using ode solvers

#1 Posted: 2020/6/4 01:40:08

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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 1260 time(s).
DoubleIntegralRK.pdf (219.12 KiB) downloaded 835 time(s).

Best regards.
Alvaro.

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frapuano 2020/6/4 04:03:00, sergio 2020/6/4 04:42:00

#2 Posted: 2020/6/7 13:21:46

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: 2020/6/7 19:50:25

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 985 time(s).

#4 Posted: 2020/6/17 20:21:22

Alvaro

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

GaussLegendreQuadrature.sm (60.58 KiB) downloaded 1258 time(s).
GaussLegendreQuadrature.pdf (160.77 KiB) downloaded 847 time(s).

Best regards.
Alvaro.

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

Yes.

DoubleIntegralSteelCat.sm (47.08 KiB) downloaded 1213 time(s).
DoubleIntegralSteelCat.pdf (105.49 KiB) downloaded 669 time(s).

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sergio 2020/6/18 05:14:00, frapuano 2020/6/18 07:33:00

#5 Posted: 2020/6/18 11:26:19

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 1010 time(s).

#6 Posted: 2020/6/18 21:35:42

Alvaro

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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 1010 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 1194 time(s).
DoubleIntegralJean.pdf (45.11 KiB) downloaded 750 time(s).

Best regards.
Alvaro

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sergio 2020/6/19 05:41:00, frapuano 2020/6/19 09:34:00

#7 Posted: 2020/6/20 07:39:28

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