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) scaricato 1450 volta(e).
DoubleIntegralRK.pdf (219,12 KiB) scaricato 1015 volta(e).

Best regards.
Alvaro.

Thanks Alvaro for your example.

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

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) scaricato 1166 volta(e).

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

GaussLegendreQuadrature.sm (60,58 KiB) scaricato 1448 volta(e).
GaussLegendreQuadrature.pdf (160,77 KiB) scaricato 1023 volta(e).

Best regards.
Alvaro.

Wrote

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

Yes.

DoubleIntegralSteelCat.sm (47,08 KiB) scaricato 1416 volta(e).
DoubleIntegralSteelCat.pdf (105,49 KiB) scaricato 837 volta(e).

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

Integrate Legendre [ Wr 24 ].sm (28,98 KiB) scaricato 1195 volta(e).

Wrote

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

Integrate Legendre [ Wr 24 ].sm (28,98 KiB) scaricato 1195 volta(e).

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) scaricato 1383 volta(e).
DoubleIntegralJean.pdf (45,11 KiB) scaricato 934 volta(e).

Best regards.
Alvaro

Wrote

Hi Jean. Yes, can copy and paste.

Thanks, Amigo !