How can we use here a Mathcad-block?
Lens-Mathcad-Block.sm (43,8 KiB) scaricato 1846 volta(e).

See too
https://en.smath.com/forum/yaf_postst25212_Lens.aspx

Wrote

How can we use here a Mathcad-block?

Here the function rkfixed() can't process the incoming expressions correctly. The block has nothing to do with it, it does not perform detailed analysis of expressions.
This is a bug in the function. The function has not been tested for this case. I can't see what's wrong here right now.

This is not a solution of the rkfixed problem, just a little playing around with X-Y plot.

Here, an option of setting the aspect ratio of the axes to 1 would be good.

File non trovato.File non trovato.

Mathcad Prime

I am wondering if there is such a kind of Mathcad Prime odesolve for solving differential equations numerically also for SMath Studio somehow?

Wrote

I am wondering if there is such a kind of Mathcad Prime odesolve for solving differential equations numerically also for SMath Studio somehow?

Not yet, but will be soon!
Question - why is the answer meters squared, and not just meters?

Wrote

I am wondering if there is such a kind of Mathcad Prime odesolve for solving differential equations numerically also for SMath Studio somehow?

What's wrong with the existing solvers?

Wrote

Wrote

I am wondering if there is such a kind of Mathcad Prime odesolve for solving differential equations numerically also for SMath Studio somehow?

What's wrong with the existing solvers?

Because odesolve in Mathcad Prime:

1. Do not require to rewrite the differential equation of a higher order into a system of first order odes

2. Determines whether a system is stiff or nonstiff and then is using accordingly the stiff numerical differential eq solver or nonstiff numerical differential eq solver

3. Can solve numerically a system of differential equations (whatever it's a system of first order differential eq or a system of higher order differential eq)

What are these existing numerical solvers of differential eq in SMath? What are the posibilities of SMath to solve numerically differential equations? Exist at least one solver that mimic the Mathcad Prime odesolve (i.e. the 3 points above menționed)?

Hi Cornel. For points 1 and 3, SMath can do what Mathcad can, and just a little more. Please, check the first post in this plugin. Can mathcad solve this odes?

RKA.sm (308,62 KiB) scaricato 2262 volta(e).
RKA.pdf (931,16 KiB) scaricato 1729 volta(e).

About point 2, one would have to review the documentation for the following plugins to see if they are capable, and to what extent, of doing what you are asking, and choose it for the solver in the SMath's solver block.

● [topic=17088]Intel ODE Solver Library[/topic]
● [topic=1918]DotNumerics[/topic]
● [topic=13809]SADEL[/topic]
● [topic=1970]Matlab C++ Math Library[/topic]
● [topic=17063]OSLO[/topic]
● [topic=17067]lsoda[/topic]
● [topic=1997]GNU Scientific Library (GSL)[/topic]

Best regards.
Alvaro.

Wrote

How can we use here a Mathcad-block?
Lens-Mathcad-Block.sm (43,8 KiB) scaricato 1846 volta(e).

See too
https://en.smath.com/forum/yaf_postst25212_Lens.aspx

Hi. dsol can solve it with this setup:



RKA-Lens.sm (179,91 KiB) scaricato 1817 volta(e).

I also use the Martin's setup for the plot.

Best regards.
Alvaro.

How to create this picture
https://en.wikipedia.org/wiki/Spherical_aberration

Hi Valery. This is a way.



spherical aberration.sm (15,88 KiB) scaricato 1807 volta(e).

Best regards.
Alvaro.

Thanks!
The last step

Hi. The screen. I also simplify a little the calculations.

spherical aberration.sm (26,41 KiB) scaricato 1958 volta(e).



Best regards.
Alvaro.

Wrote

Hi Valery. This is a way.

...

spherical aberration.sm (15,88 KiB) scaricato 1807 volta(e).

Best regards.
Alvaro.

Very elegant solution

Root-free version of the spherical lens


spherical aberration_Kr.sm (12,37 KiB) scaricato 1741 volta(e).

Wrote

Very elegant solution

Gracias Oscar! Pero espérate tantito nomás para que veas lo que puede hacer un doc alemán.

Thanks Oscar! But wait a little longer so you can see what a German doctor can do.

Best regards.
Alvaro.