Wrote

Wrote

Sorry Jean, no graph, only values...

... from enough values: we can best approximate/graph !!!

I'll try to explain myself better: a value for each unknown, so 3 values...

Wrote

I'll try to explain myself better: a value for each unknown, so 3 values...

You mentioned Jacobian could solve.
Then, tabulate row wise those Jacobian 3 values ?

Wrote

Maybe you can try to beat the horse otherwise.

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Jean this screenshot comes from your example.



You are right, Ed, CLS and As are all independent.

My unknown are eG, Xx and Xy. NEd, MxEd and MyEd are assigned, I can't change their values. So I do not understand your suggestion: how can I have a better estimates of unknown throught U,V,W?

In yellow I reported the solution of the sistem from my textbook (found using Excel and Mathcad): equations values are quite close to zero, so the procedure works correctly. It seems that the only way to refine the solution, is to manually change the guessed values... not very nice

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Hi. In the attached, a numerical procedure for double integrals using rkfixed ode solver.

With some improvements maybe this idea can be used instead sums. Also, it can be modified for accept units.

Forum example w-o units_4-BIS.sm (64 КиБ) скачан 53 раз(а).

Best regards.
Alvaro.

Using rkfixed it do not end. I'll try using your RK23...

Wrote

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Hi. In the attached, a numerical procedure for double integrals using rkfixed ode solver.

With some improvements maybe this idea can be used instead sums. Also, it can be modified for accept units.

Forum example w-o units_4-BIS.sm (64 КиБ) скачан 53 раз(а).

Best regards.
Alvaro.

Using rkfixed it do not end. I'll try using your RK23...

The RK23 procedure it's very fast but I obtain a strange solution.
I used also al_rkadapt but the solver do not ends...

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Your last today message has disappeared ???
It happens sometimes ... ?
You can solve for either or all X,Y,Z
from some given conditions [U,V,W].
The problem is ill posed from the onset.
Only trig functions are approximated in radians.
Otherwise, maths are units less.
Some solvers are exclusive of units, others have reserved
variable name. Thus: eradicate units and subscript gyzmas.
Can't find variables, units don't match ...
Can you plot the innermost integral like usual ?
If you can't => there is no project yet.

Wrote

Wrote

Wrote

Hi. In the attached, a numerical procedure for double integrals using rkfixed ode solver.

With some improvements maybe this idea can be used instead sums. Also, it can be modified for accept units.

Forum example w-o units_4-BIS.sm (64 КиБ) скачан 53 раз(а).

Best regards.
Alvaro.

Using rkfixed it do not end. I'll try using your RK23...

The RK23 procedure it's very fast but I obtain a strange solution.
I used also al_rkadapt but the solver do not ends...

Forum example w-o units_4-RK23.sm (72 КиБ) скачан 41 раз(а).
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It seems that unkonown variables were lost with this numerical procedure

Wrote

...
It seems that unkonown variables were lost with this numerical procedure

Hi. Yes, that's what probably it's happen. I try different configurations but can't find none good enough. You can avoid the evaluation at the time of the definition by addint the line command:



Same thing for use DInt function.

My experience for the civil engineering worksheets is that the best choice is use heaviside step for piecewise functions instead inequalities or if and symbolic evaluation for the integrals because in mathcad the numerical procedures for evaluating piecewise integrals are not good. But this can't be done in SMath. Here you can read an example about this problem (there are others about civil eng calculus, but can't fin them): https://community.ptc.com/t5/PTC-Mathcad/Plots-for-Conditional-Function/td-p/124048/page/2

I'm also try to analyze the answer from Martin about using Maxima with heaviside, but again can't get a practical solution, here for the use of solve. Looks that in Maxima, like in Mathcad Prime, there are not correspondence between heaviside in symbolics with the numerical procedures. And this can't be a surprise: heaviside isn't a function, and can't be numerically evaluate like functions.

For a pure numerical application I guess that you need to found a numerical procedure that can handle discontinuities above the integral sign. But for double integrals this could be very slow or inaccurate, like RK23 with a low number of iterations.

Another option could be pass as parameters for the numerical procedure the values of the jumps and integrate between them.

Best regards.
Alvaro.

... group the solutions.

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Wrote

Hello everyone,
I would like to solve a system of two equations in two variables (x, y) which contain defined integrals with other two variables (t, z for example).

The functions seem to work properly, but why does Smath also recognize as unknowns the fictitious variables into the integrals?
I can't solve the system....


Thanks.

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I don0t know if you got this response, but using Algsys provided in the Máxima plugin I could resolve your problem

Wrote

I don0t know if you got this response, but using Algsys provided in the Máxima plugin I could resolve your problem

...... Post # 1
Hello everyone,
I would like to solve a system of two equations in two variables (x, y) which contain defined integrals with other two variables (t, z for example).

The functions seem to work properly, but why does Smath also recognize as unknowns the fictitious variables into the integrals ?
I can't solve the system....

The setup is ill posed for solving intersection of two
functions f(x,y) ... g(x,y) this last one missing.
g(x,y) can be anything crossing f(x,y) at least once.

Page3 Prova funzione.sm (16 КиБ) скачан 23 раз(а).

Wrote

I don't know if you got this response, but using Algsys provided in the Máxima plugin I could resolve your problem

What's wrong/missing from native Smath ?

Solve FindRoot [f(x,y) ... g(x,y)].sm (15 КиБ) скачан 31 раз(а).