differential equations

#21 Pubblicato: 26/12/2019 18:32:57

0 apprezzamenti in 35 post.

Gruppo: User

Hi, sorry but I have practically no experience with this program and I find it difficult to understand the functions.
If you can please explain the various steps to be able to solve the differential equation in the picture.
I am interested in deriving the function phi (t), what do you need to know to solve the differential equation?
Thanks for your patience

Documento2 DE [explain more] (25).sm (48,29 KiB) scaricato 1181 volta(e).

#22 Pubblicato: 26/12/2019 22:53:48

Jean Giraud

983 apprezzamenti in 6.866 post.

Gruppo: User

Wrote
sorry but I have practically no experience with this program and I find it difficult to understand the functions.
If you can please explain the various steps to be able to solve the differential equation in the picture.
I am interested in deriving the function phi (t), what do you need to know to solve the differential equation?
T

The setup to numerical DE solver is same as Mathcad,
even superior as it takes the parameters as vector.
Use p[1,2,3] for those parameters.
Up to what you proposed before: you don't have a DE
Those parameters are non-sense as they send the system in the zillion domain. Get that DE from the teacher, a bit of abstract would help.

Documento2 DE [explain more] (25).sm (71,7 KiB) scaricato 1160 volta(e).

#23 Pubblicato: 27/12/2019 01:03:26

Alvaro

1.139 apprezzamenti in 1.805 post.

Gruppo: User

Wrote
...
I am interested in deriving the function phi (t), what do you need to know to solve the differential equation?
Thanks for your patience

Hi. Usually we want know the ode and it's initial conditions. In your case you have boundary conditions, which can be solved by the shooting method.

Hope this helps.

motocicleta.sm (48,71 KiB) scaricato 1343 volta(e).
motocicleta.pdf (203,43 KiB) scaricato 871 volta(e).

Best regards.
Alvaro.

2 utenti hanno apprezzato questo post

frapuano 27/12/2019 05:52:00, sergio 27/12/2019 07:39:00

#24 Pubblicato: 27/12/2019 07:45:06

Ale16595

0 apprezzamenti in 35 post.

Gruppo: User

My initial conditions are:

-phi(t = 0) = 0.146

-phi'(t = 0) = 0

#25 Pubblicato: 27/12/2019 08:06:25

Alvaro

1.139 apprezzamenti in 1.805 post.

Gruppo: User

Wrote
My initial conditions are:

-phi(t = 0) = 0.146

-phi'(t = 0) = 0

For a Cauchy problem it's more easy.

motocicleta with IC.sm (37,14 KiB) scaricato 1332 volta(e).
motocicleta with IC.pdf (136,74 KiB) scaricato 883 volta(e).

Best regards.
Alvaro.

3 utenti hanno apprezzato questo post

Ale16595 27/12/2019 08:25:00, frapuano 27/12/2019 08:46:00, Вячеслав Мезенцев 27/12/2019 13:43:00

#26 Pubblicato: 27/12/2019 08:26:00

Ale16595

0 apprezzamenti in 35 post.

Gruppo: User

Thank you very much,
regards

#27 Pubblicato: 27/12/2019 13:12:31

Jean Giraud

983 apprezzamenti in 6.866 post.

Gruppo: User

This is an offer ... accept/reject ... go back to "square zero"
1. What maths are given/invented: a formula ?
2. From that formula, what is next
So, you have a formula and an objective project,
i.e: a pretty short work sheet not yet circular in the blue.
Jean

1 utenti hanno apprezzato questo post

Ale16595 27/12/2019 14:06:00

#28 Pubblicato: 27/12/2019 14:05:46

Ale16595

0 apprezzamenti in 35 post.

Gruppo: User

Wrote
This is an offer ... accept/reject ... go back to "square zero"
1. What maths are given/invented: a formula ?
2. From that formula, what is next
So, you have a formula and an objective project,
i.e: a pretty short work sheet not yet circular in the blue.
Jean

I appreciate the advice. I'm trying to learn

#29 Pubblicato: 27/12/2019 15:51:08

Jean Giraud

983 apprezzamenti in 6.866 post.

Gruppo: User

Wrote
I appreciate the advice. I'm trying to learn

Just give the formula that you were given.
or make an image from source ... learning is after.

#30 Pubblicato: 27/12/2019 22:26:30

Jean Giraud

983 apprezzamenti in 6.866 post.

Gruppo: User

Read more about ODE ... just an initiating visit.
These two examples are Cauchy integration. They have no formal symbolic.
A discrete integration is possible via the module rkf4(y0,x0,x1,n,f).
From there: easy to get the discrete derivative.
Jean

ODE Cauchy Project.sm (27,38 KiB) scaricato 1369 volta(e).

#31 Pubblicato: 28/12/2019 18:49:56

Ale16595

0 apprezzamenti in 35 post.

Gruppo: User

Hi, sorry if I bother you again. I'm trying to integrate a function, the function in question is psi''(t) in order to derive psi'(t).
I tried using Simpson and Romberg's recursive methods, but without getting a solution.
Where am I wrong?

PROJECT.sm (69,12 KiB) scaricato 1386 volta(e).

#32 Pubblicato: 28/12/2019 21:59:18

Jean Giraud

983 apprezzamenti in 6.866 post.

Gruppo: User

Wrote
Hi, sorry if I bother you again. I'm trying to integrate a function, the function in question is psi''(t) in order to derive psi'(t).

You have phi in your document ... psi is a built-in function.
So, if phi''(t) is the 2nd derivative ... then the derivative
is simply the integral. To expedite fast: done discrete.
If you have questions: please re-post this document.
Cheers ... Jean.

PROJECT [1].sm (30,82 KiB) scaricato 1143 volta(e).

#33 Pubblicato: 28/12/2019 23:19:45

Jean Giraud

983 apprezzamenti in 6.866 post.

Gruppo: User

Wrote
You have phi in your document

.... in fact you have PSI''(t).
Maple does not find an explicit integral.

PROJECT [1].sm (21,91 KiB) scaricato 1159 volta(e).

#34 Pubblicato: 29/12/2019 09:18:44

Jean Giraud

983 apprezzamenti in 6.866 post.

Gruppo: User

... lot more maths in there.

PROJECT [1].sm (44,37 KiB) scaricato 1168 volta(e).

#35 Pubblicato: 29/12/2019 11:16:00

Alvaro

1.139 apprezzamenti in 1.805 post.

Gruppo: User

Wrote
Hi, sorry if I bother you again. I'm trying to integrate a function, the function in question is psi''(t) in order to derive psi'(t).
I tried using Simpson and Romberg's recursive methods, but without getting a solution.
Where am I wrong?

PROJECT.sm (69,12 KiB) scaricato 1386 volta(e).

Hi. You can use any Runge Kutta solver for integration.

Also, you can use SMath int procedure, but it's very (very) slow:

For the theory, remember that you can integrate (with definite integrals) both sides of an equation and get an equality too, which don't work with derivatives.

PROJECT.sm (74,9 KiB) scaricato 1396 volta(e).

Best regards.
Alvaro.

1 utenti hanno apprezzato questo post

frapuano 29/12/2019 14:27:00

#36 Pubblicato: 29/12/2019 11:21:10

Ale16595

0 apprezzamenti in 35 post.

Gruppo: User

Hi, I have calculated the function psi '(t) through dn_GearsBDF.
But now I can't calculate the ratio in the picture.

The error says, "The matrix must be square"
PROJECT.sm (57,24 KiB) scaricato 1382 volta(e).

#37 Pubblicato: 29/12/2019 14:19:55

Jean Giraud

983 apprezzamenti in 6.866 post.

Gruppo: User

Wrote
Hi, I have calculated the function psi '(t) through dn_GearsBDF.
But now I can't calculate the ratio in the picture.

Result from numerical ODE solvers is a data set.
Generate an interpolation scalar to 'x' ... then plot.
@ the end of the document ... more questions: -this one.

PROJECT (1).sm (74,9 KiB) scaricato 1376 volta(e).

Forum SMath

differential equations - solve differential equations - Messaggi