differential equations

#21 Posted: 12/26/2019 6:32:57 PM

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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 KiB) downloaded 41 time(s).

#22 Posted: 12/26/2019 10:53:48 PM

Jean Giraud

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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 KiB) downloaded 34 time(s).

#23 Posted: 12/27/2019 1:03:26 AM

Alvaro Diaz Falconi

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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 KiB) downloaded 40 time(s).
motocicleta.pdf (203 KiB) downloaded 51 time(s).

Best regards.
Alvaro.

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

#24 Posted: 12/27/2019 7:45:06 AM

Ale16595

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My initial conditions are:

-phi(t = 0) = 0.146

-phi'(t = 0) = 0

#25 Posted: 12/27/2019 8:06:25 AM

Alvaro Diaz Falconi

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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 KiB) downloaded 47 time(s).
motocicleta with IC.pdf (136 KiB) downloaded 54 time(s).

Best regards.
Alvaro.

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Ale16595 12/27/2019 8:25:00 AM, frapuano 12/27/2019 8:46:00 AM, Вячеслав Мезенцев 12/27/2019 1:43:00 PM

#26 Posted: 12/27/2019 8:26:00 AM

Ale16595

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Thank you very much,
regards

#27 Posted: 12/27/2019 1:12:31 PM

Jean Giraud

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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

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Ale16595 12/27/2019 2:06:00 PM

#28 Posted: 12/27/2019 2:05:46 PM

Ale16595

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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 Posted: 12/27/2019 3:51:08 PM

Jean Giraud

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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 Posted: 12/27/2019 10:26:30 PM

Jean Giraud

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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 KiB) downloaded 43 time(s).

#31 Posted: 12/28/2019 6:49:56 PM

Ale16595

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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 KiB) downloaded 37 time(s).

#32 Posted: 12/28/2019 9:59:18 PM

Jean Giraud

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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 KiB) downloaded 29 time(s).

#33 Posted: 12/28/2019 11:19:45 PM

Jean Giraud

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You have phi in your document

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

PROJECT [1].sm (21 KiB) downloaded 34 time(s).

#34 Posted: 12/29/2019 9:18:44 AM

Jean Giraud

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... lot more maths in there.

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#35 Posted: 12/29/2019 11:16:00 AM

Alvaro Diaz Falconi

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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 KiB) downloaded 37 time(s).

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 KiB) downloaded 36 time(s).

Best regards.
Alvaro.

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frapuano 12/29/2019 2:27:00 PM

#36 Posted: 12/29/2019 11:21:10 AM

Ale16595

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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 KiB) downloaded 31 time(s).

#37 Posted: 12/29/2019 2:19:55 PM

Jean Giraud

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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 KiB) downloaded 40 time(s).

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