Wrote

I have solved one equation in sage math but not able understand how to solve in smath anybody can guide me on this. below is my equation

exercise1

r = var('r')
PI = pi.n()
rc = 281
rw = 262
Bc = 36/180*PI
F = (r^2-rw^2)*sqrt(rc^2-r^2*sin(Bc)^2)/sqrt((rc^2-rw^2)^2*rc^2*cos(Bc)^2-(r^2-rw^2)^2*(rc^2-r^2*sin(Bc)^2))
F.show()

z = function('z',r)
d = desolve_rk4(diff(z,r)-F,z,ics=[rc,0],end_points=255,step=-0.01)
list_plot(d,plotjoined=True, aspect_ratio=1)

Try this.

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ODE example.sm (8 КиБ) скачан 97 раз(а).

Wrote

This also means that those who installed ODESolvers plug-in before 17 August 2015 will never see any updates of this plug-in and will always use outdated version. That is why I think SMath Studio message you mentioned is a good thing. I suggest to delete installed version of ODESolvers plug-in (using Extensions Manager - select plug-in and press uninstall button at the bottom of the dialog) and then install it again.

Best regards, Andrey Ivashov.

Please, uninstall and install the plugin again.

Wrote

I have solved one equation in sage math but not able understand how to solve in smath anybody can guide me on this. below is my equation

_____________________________

Commonly, many are confused with RK's. RK's does not output the integral curve.
They output the "cumulative area". They belong to the class "Lagrangian methods".
RK's are NOT solvers, RK's are "Integrators". They are considered more exact than
the simple Finite Differences. Very useful for integrating "systems".

Here is your example in Smath 5346 [April 2014].

Jean

ODE RK4 Example.sm (17 КиБ) скачан 79 раз(а).

... suite:

I have sanity checked your example, bad news: RK4 is very inaccurate.
Why is that so ? RK's are "ping pong" pieces of polynomials. Thus
turning affected by the large range of the 'x' variate. For ultimate
accuracy in this simple example, you can use the "Romberg" integrator.
This integrator works in the 0..1 range, scaled back to the 'x' range.
From various testing, I have categorised Romberg accurate to 12...15
decimals. In Scientific/Engineering works, the RK4 example is not
the best candidate. The Romberg= data is disabled, it takes few minutes.

Jean

ODE RK4 Example.sm (24 КиБ) скачан 78 раз(а).

Jean,

We all know that rkfixed() is not accurate, why you did not use Rkadapt() as usual we do in Mathcad?

Regards,
Ra

EDIT: BTW, If Romberg was activated in the recent SMath, it will be solved in few seconds (not in few minutes as mentioned)

Moreover, if you use lower number of steps ( "4:number" ), for example if you use 20:

sol:= Rkadapt([0],255,280,20,D(x,y))

Rkadapt will fail with the error: "Index was outside the the bonds of the array". I know that uni made these two functions rkfixed() and Rkadapt() quite long time ago, and he also made much better ODE solvers in the meantime

Wrote

Jean,

We all know that rkfixed() is not accurate, why you did not use Rkadapt() as usual we do in Mathcad?

Regards,
Ra

Can't be more right Radovan, thanks for the comment.
1. Refactored a bit
2. Lorenz attractor Rkadapt added.
This attractor was animated last week [visit: Lorenz attractor]

Have a good day, Jean

ODE [rk4, Rkadapt, Lorenz].sm (37 КиБ) скачан 98 раз(а).

Updated for the fully automatic build using Release Manager.

Installing ODE Solvers plugin this is causing forced close on Arch Linux + Mono.
After forced close you cannot be able to open Smath again unless manually deleting the plugin.

Regards

Because the plugin is not compatible with Linux + Mono:

Цитата

Intel ODE Solvers Library (VS2013 + VS2008, .Net 2.0, C#, C++/CLI, Win32 + x64).

Win32 + x64 - means Windows only, C++/CLI - unmanaged code used.

Updated. Skip intel ode assembly loading if Linux used. So in Linux only 2 functions available: rkfixed() and Rkadapt().

Raspbian on RaspberryPi 3.

Simple intel ode test 2.

[albumimg]1500[/albumimg]

iode.test2.sm (22 КиБ) скачан 126 раз(а).
iode.test2.pdf (121 КиБ) скачан 98 раз(а).

Updated. Fixed issue with zero point.

ODE test 3. Something wrong with Rkadapt().

[albumimg]1526[/albumimg]

iode.test3.sm (24 КиБ) скачан 54 раз(а).
iode.test3.pdf (112 КиБ) скачан 52 раз(а).

Wrote

ODE test 3. Something wrong with Rkadapt().

Hi Viacheslav. It seems that for Rkadapt t repeats itself, at least for low N values. Maybe you can handle that with some if abs(t[n+1]-t[n])<(some tol) then do something for modify t, and not add it to the final solution. Probably it could be because your step size goes too short.



Best regards.
Alvaro.

PD: I try to use albuming for the image, but fails.

Wrote

ODE test 3. Something wrong with Rkadapt().

Nothing more deceiving than experimenting ODEsolve.
The attached is worth the visit !

ODE Yuk.sm (28 КиБ) скачан 58 раз(а).

Wrote

Nothing more deceiving than experimenting ODEsolve.
The attached is worth the visit !

This one is interesting as well

ODE_0 Rkadapt Analyze.sm (40 КиБ) скачан 52 раз(а).

Wrote

Hi Viacheslav. It seems that for Rkadapt t repeats itself, at least for low N values.

It looks OK to me from Rkadapt design.
It reaches solution in 42 steps vs fixed 100.

iode.test3 Strip Rkadapt.sm (11 КиБ) скачан 49 раз(а).

Wrote

It reaches solution in 42 steps vs fixed 100.

... In fact: Rkadapt reaches solution in 35 steps.
MCD Rkadapt results in equally spaced solutions.
MCD rkadapt comes with two extra parameters
"acc" accuracy
"s" step size
As it looks Smath Rkadapt muffs the start,
Try 34/35 => observe the result.

iode.test3 Strip Rkadapt.sm (16 КиБ) скачан 49 раз(а).

Wrote

ODE test 3. Something wrong with Rkadapt().

Here is another oddity: NO Smath ODE solvers cope with the 'Floor".

ODE rkfixed Pulse Pitfall.sm (57 КиБ) скачан 59 раз(а).

Wrote

Wrote

ODE test 3. Something wrong with Rkadapt().

Hi Viacheslav. It seems that for Rkadapt t repeats itself, at least for low N values. Maybe you can handle that with some if abs(t[n+1]-t[n])<(some tol) then do something for modify t, and not add it to the final solution. Probably it could be because your step size goes too short.

Wrote

MCD rkadapt comes with two extra parameters
"acc" accuracy
"s" step size

Hi. Probably, acc = (some tol) and s = minimun step size, in case that s = s/2 is too small.

Best regards.
Alvaro.

Wrote

ODE test 3. Something wrong with Rkadapt().

Thanks Viacheslav for your dedication,

There is no such test function wrt ODE solvers. Each case is specific.
This is so true that the specific Radau ODE solver was designed for HIRES.
Many projects need fixed steps, other are solved via Rkadapt.
YUK & RK4 lasted quite a while in the Mathsoft Collaboratory.
They are reliable, again no way to verdict with others w/o test reference data.

Cheers ... Jean

Integral 0000 f(x,t) RK4 [Short] Copy.sm (71 КиБ) скачан 46 раз(а).