Double Integration using ode solvers

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

1,106 likes in 1,784 posts.

Group: User

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 1150 time(s).
DoubleIntegralRK.pdf (219.12 KiB) downloaded 734 time(s).

Best regards.
Alvaro.

2 users liked this post

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

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

SteelCat

3 likes in 47 posts.

Group: User

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

983 likes in 6,866 posts.

Group: User

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 897 time(s).

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

Alvaro

1,106 likes in 1,784 posts.

Group: User

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

GaussLegendreQuadrature.sm (60.58 KiB) downloaded 1149 time(s).
GaussLegendreQuadrature.pdf (160.77 KiB) downloaded 687 time(s).

Best regards.
Alvaro.

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

Yes.

DoubleIntegralSteelCat.sm (47.08 KiB) downloaded 1103 time(s).
DoubleIntegralSteelCat.pdf (105.49 KiB) downloaded 585 time(s).

2 users liked this post

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

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

Jean Giraud

983 likes in 6,866 posts.

Group: User

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 918 time(s).

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

Alvaro

1,106 likes in 1,784 posts.

Group: User

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) downloaded 918 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 1073 time(s).
DoubleIntegralJean.pdf (45.11 KiB) downloaded 649 time(s).

Best regards.
Alvaro

2 users liked this post

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

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

Jean Giraud

983 likes in 6,866 posts.

Group: User

Wrote
Hi Jean. Yes, can copy and paste.

Thanks, Amigo !

SMath Forum

Double Integration using ode solvers - Messages