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Offline uni  
#61 Posted : 08 October 2015 08:28:39(UTC)
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Originally Posted by: madan26 Go to Quoted Post
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'Wink
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.
File Attachment(s):
ODE example.sm (9kb) downloaded 74 time(s).
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Offline uni  
#62 Posted : 05 September 2016 20:09:30(UTC)
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Originally Posted by: Andrey Ivashov Go to Quoted Post
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who installed ODESolvers plug-in before 17 August 2015 will never see any updates of this plug-in and will always use outdated version.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.
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Offline Jean Giraud  
#63 Posted : 06 September 2016 07:01:43(UTC)
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Originally Posted by: uni Go to Quoted Post
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 (18kb) downloaded 56 time(s).

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Offline Jean Giraud  
#64 Posted : 06 September 2016 08:01:49(UTC)
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... 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 (25kb) downloaded 59 time(s).


Offline omorr  
#65 Posted : 06 September 2016 08:32:07(UTC)
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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 Good

Edited by user 06 September 2016 14:28:59(UTC)  | Reason: Not specified

When Sisyphus climbed to the top of a hill, they said: "Wrong boulder!"
Offline Jean Giraud  
#66 Posted : 06 September 2016 15:39:21(UTC)
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Originally Posted by: omorr Go to Quoted Post
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 (38kb) downloaded 75 time(s).

Offline uni  
#67 Posted : 16 September 2016 16:40:33(UTC)
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Updated for the fully automatic build using Release Manager.
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on 16/09/2016(UTC)
Offline overlord  
#68 Posted : 23 June 2018 23:53:16(UTC)
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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
Offline uni  
#69 Posted : 24 June 2018 00:34:17(UTC)
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Because the plugin is not compatible with Linux + Mono:

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


Win32 + x64 - means Windows only, C++/CLI - unmanaged code used.
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Offline uni  
#70 Posted : 19 July 2018 13:45:36(UTC)
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Updated. Skip intel ode assembly loading if Linux used. So in Linux only 2 functions available: rkfixed() and Rkadapt().

Raspbian on RaspberryPi 3.

2018-07-19_15-43-48.png
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Offline uni  
#71 Posted : 01 August 2018 19:12:03(UTC)
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Simple intel ode test 2.



iode.test2.sm (23kb) downloaded 79 time(s).
iode.test2.pdf (122kb) downloaded 61 time(s).

Edited by user 24 December 2018 11:55:44(UTC)  | Reason: Not specified

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Offline uni  
#72 Posted : 03 December 2018 23:21:26(UTC)
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Updated. Fixed issue with zero point.

ODE test 3. Something wrong with Rkadapt().



iode.test3.sm (25kb) downloaded 33 time(s).
iode.test3.pdf (113kb) downloaded 32 time(s).
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Offline Razonar  
#73 Posted : 04 December 2018 05:32:02(UTC)
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Originally Posted by: uni Go to Quoted Post


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.

Clipboard01.gif

Best regards.
Alvaro.

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

Edited by user 04 December 2018 05:36:58(UTC)  | Reason: Not specified

Offline Jean Giraud  
#74 Posted : 04 December 2018 07:40:00(UTC)
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Originally Posted by: uni Go to Quoted Post
ODE test 3. Something wrong with Rkadapt().


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

ODE Yuk.sm (29kb) downloaded 34 time(s).
Offline Jean Giraud  
#75 Posted : 04 December 2018 07:43:31(UTC)
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Originally Posted by: Jean Giraud Go to Quoted Post
Nothing more deceiving than experimenting ODEsolve.
The attached is worth the visit !


This one is interesting as well

ODE_0 Rkadapt Analyze.sm (41kb) downloaded 30 time(s).
Offline Jean Giraud  
#76 Posted : 04 December 2018 15:55:44(UTC)
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Originally Posted by: Razonar Go to Quoted Post
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 (12kb) downloaded 28 time(s).
Offline Jean Giraud  
#77 Posted : 04 December 2018 16:17:01(UTC)
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Originally Posted by: Jean Giraud Go to Quoted Post
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 (17kb) downloaded 28 time(s).

Offline Jean Giraud  
#78 Posted : 04 December 2018 16:31:24(UTC)
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Originally Posted by: uni Go to Quoted Post
ODE test 3. Something wrong with Rkadapt().


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

ODE rkfixed Pulse Pitfall.sm (58kb) downloaded 35 time(s).
Offline Razonar  
#79 Posted : 04 December 2018 18:10:00(UTC)
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Originally Posted by: Razonar Go to Quoted Post
Originally Posted by: uni Go to Quoted Post


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.


Originally Posted by: Jean Giraud Go to Quoted Post

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.
Offline Jean Giraud  
#80 Posted : 05 December 2018 21:34:53(UTC)
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Originally Posted by: uni Go to Quoted Post
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 (72kb) downloaded 30 time(s).
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