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Originally Posted by: madan26  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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Viacheslav N. Mezentsev |
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Rank: Advanced Member Groups: Registered, Advanced Member Joined: 10/11/2010(UTC) Posts: 1,549 Was thanked: 1309 time(s) in 767 post(s)
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Originally Posted by: Andrey Ivashov 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who installed ODESolvers plug-in before 17 August 2015 will never see any updates of this plug-in and will always use outdated version.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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Viacheslav N. Mezentsev |
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Originally Posted by: uni 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 60 time(s).
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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 63 time(s).
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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  Edited by user 06 September 2016 14:28:59(UTC)
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When Sisyphus climbed to the top of a hill, they said: "Wrong boulder!" |
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Originally Posted by: omorr 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 78 time(s).
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Updated for the fully automatic build using Release Manager. |
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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
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Rank: Advanced Member Groups: Registered, Advanced Member Joined: 10/11/2010(UTC) Posts: 1,549 Was thanked: 1309 time(s) in 767 post(s)
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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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Viacheslav N. Mezentsev |
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Rank: Advanced Member Groups: Registered, Advanced Member Joined: 10/11/2010(UTC) Posts: 1,549 Was thanked: 1309 time(s) in 767 post(s)
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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.  |
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Viacheslav N. Mezentsev |
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Rank: Advanced Member Groups: Registered, Advanced Member Joined: 10/11/2010(UTC) Posts: 1,549 Was thanked: 1309 time(s) in 767 post(s)
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Viacheslav N. Mezentsev |
1 user thanked uni for this useful post.
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Rank: Advanced Member Groups: Registered, Advanced Member Joined: 10/11/2010(UTC) Posts: 1,549 Was thanked: 1309 time(s) in 767 post(s)
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Viacheslav N. Mezentsev |
1 user thanked uni for this useful post.
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Originally Posted by: uni
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. Edited by user 04 December 2018 05:36:58(UTC)
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Originally Posted by: uni ODE test 3. Something wrong with Rkadapt(). Nothing more deceiving than experimenting ODEsolve. The attached is worth the visit ! ODE Yuk.sm (29kb) downloaded 39 time(s).
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Originally Posted by: Jean Giraud 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 34 time(s).
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Originally Posted by: Razonar 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 33 time(s).
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Originally Posted by: Jean Giraud 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 32 time(s).
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Originally Posted by: uni 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 39 time(s).
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Originally Posted by: Razonar Originally Posted by: uni
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
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.
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Originally Posted by: uni 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 32 time(s).
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