differential equations

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

0 me gusta en 35 mensajes.

Grupo: 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) descargado 1177 vez(es).

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

Jean Giraud

983 me gusta en 6.866 mensajes.

Grupo: 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) descargado 1156 vez(es).

#23 Publicado: 27/12/2019 1:03:26

Alvaro

1.139 me gusta en 1.805 mensajes.

Grupo: 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) descargado 1339 vez(es).
motocicleta.pdf (203,43 KiB) descargado 864 vez(es).

Best regards.
Alvaro.

A 2 usuarios les gustó este mensaje

frapuano 27/12/2019 5:52:00, sergio 27/12/2019 7:39:00

#24 Publicado: 27/12/2019 7:45:06

Ale16595

0 me gusta en 35 mensajes.

Grupo: User

My initial conditions are:

-phi(t = 0) = 0.146

-phi'(t = 0) = 0

#25 Publicado: 27/12/2019 8:06:25

Alvaro

1.139 me gusta en 1.805 mensajes.

Grupo: 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) descargado 1328 vez(es).
motocicleta with IC.pdf (136,74 KiB) descargado 877 vez(es).

Best regards.
Alvaro.

A 3 usuarios les gustó este mensaje

Ale16595 27/12/2019 8:25:00, frapuano 27/12/2019 8:46:00, Вячеслав Мезенцев 27/12/2019 13:43:00

#26 Publicado: 27/12/2019 8:26:00

Ale16595

0 me gusta en 35 mensajes.

Grupo: User

Thank you very much,
regards

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

Jean Giraud

983 me gusta en 6.866 mensajes.

Grupo: 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

A 1 usuarios les gustó este mensaje

Ale16595 27/12/2019 14:06:00

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

Ale16595

0 me gusta en 35 mensajes.

Grupo: 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 Publicado: 27/12/2019 15:51:08

Jean Giraud

983 me gusta en 6.866 mensajes.

Grupo: 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 Publicado: 27/12/2019 22:26:30

Jean Giraud

983 me gusta en 6.866 mensajes.

Grupo: 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) descargado 1369 vez(es).

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

Ale16595

0 me gusta en 35 mensajes.

Grupo: 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) descargado 1384 vez(es).

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

Jean Giraud

983 me gusta en 6.866 mensajes.

Grupo: 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) descargado 1141 vez(es).

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

Jean Giraud

983 me gusta en 6.866 mensajes.

Grupo: 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) descargado 1153 vez(es).

#34 Publicado: 29/12/2019 9:18:44

Jean Giraud

983 me gusta en 6.866 mensajes.

Grupo: User

... lot more maths in there.

PROJECT [1].sm (44,37 KiB) descargado 1166 vez(es).

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

Alvaro

1.139 me gusta en 1.805 mensajes.

Grupo: 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) descargado 1384 vez(es).

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) descargado 1396 vez(es).

Best regards.
Alvaro.

A 1 usuarios les gustó este mensaje

frapuano 29/12/2019 14:27:00

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

Ale16595

0 me gusta en 35 mensajes.

Grupo: 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) descargado 1380 vez(es).

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

Jean Giraud

983 me gusta en 6.866 mensajes.

Grupo: 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) descargado 1372 vez(es).

Foro SMath

differential equations - solve differential equations - Mensajes