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 839 time(s).
DoubleIntegralRK.pdf (219.12 KiB) downloaded 501 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 638 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 803 time(s).
GaussLegendreQuadrature.pdf (160.77 KiB) downloaded 455 time(s).

Best regards.
Alvaro.

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

Yes.

DoubleIntegralSteelCat.sm (47.08 KiB) downloaded 763 time(s).
DoubleIntegralSteelCat.pdf (105.49 KiB) downloaded 392 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 667 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 667 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 756 time(s).
DoubleIntegralJean.pdf (45.11 KiB) downloaded 439 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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