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 uni #61 Posted : 08 October 2015 08:28:39(UTC) Rank: Advanced MemberGroups: Registered, Advanced MemberJoined: 10/11/2010(UTC)Posts: 1,508Was thanked: 1285 time(s) in 750 post(s) 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 equationexercise1r = var('r'PI = pi.n()rc = 281rw = 262Bc = 36/180*PIF = (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 77 time(s). Russia ☭ forever Viacheslav N. Mezentsev
 uni #62 Posted : 05 September 2016 20:09:30(UTC) Rank: Advanced MemberGroups: Registered, Advanced MemberJoined: 10/11/2010(UTC)Posts: 1,508Was thanked: 1285 time(s) in 750 post(s) 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who installed ODESolvers plug-in before 17 August 2015 will never see any updates of this plug-in and will always use outdated version.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. Russia ☭ forever Viacheslav N. Mezentsev
 Jean Giraud #63 Posted : 06 September 2016 07:01:43(UTC) Rank: GuestGroups: Registered Joined: 04/07/2015(UTC)Posts: 6,866Was thanked: 983 time(s) in 811 post(s) 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 thanthe 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). 1 user thanked Jean Giraud for this useful post. on 06/09/2016(UTC)
 Jean Giraud #64 Posted : 06 September 2016 08:01:49(UTC) Rank: GuestGroups: Registered Joined: 04/07/2015(UTC)Posts: 6,866Was thanked: 983 time(s) in 811 post(s) ... 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. Thusturning affected by the large range of the 'x' variate. For ultimateaccuracy 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...15decimals. In Scientific/Engineering works, the RK4 example is notthe best candidate. The Romberg= data is disabled, it takes few minutes.Jean ODE RK4 Example.sm (25kb) downloaded 63 time(s).
 omorr #65 Posted : 06 September 2016 08:32:07(UTC) Rank: AdministrationGroups: Registered, Advanced MemberJoined: 23/06/2009(UTC)Posts: 1,740Was thanked: 318 time(s) in 268 post(s) 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)  | Reason: Not specified When Sisyphus climbed to the top of a hill, they said: "Wrong boulder!"
 Jean Giraud #66 Posted : 06 September 2016 15:39:21(UTC) Rank: GuestGroups: Registered Joined: 04/07/2015(UTC)Posts: 6,866Was thanked: 983 time(s) in 811 post(s) 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,RaCan't be more right Radovan, thanks for the comment.1. Refactored a bit2. 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).
 uni #67 Posted : 16 September 2016 16:40:33(UTC) Rank: Advanced MemberGroups: Registered, Advanced MemberJoined: 10/11/2010(UTC)Posts: 1,508Was thanked: 1285 time(s) in 750 post(s) Updated for the fully automatic build using Release Manager. Russia ☭ forever Viacheslav N. Mezentsev 1 user thanked uni for this useful post. on 16/09/2016(UTC)
 overlord #68 Posted : 23 June 2018 23:53:16(UTC) Rank: Advanced MemberGroups: Registered Joined: 23/07/2013(UTC)Posts: 1,154Was thanked: 526 time(s) in 352 post(s) 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
 uni #69 Posted : 24 June 2018 00:34:17(UTC) Rank: Advanced MemberGroups: Registered, Advanced MemberJoined: 10/11/2010(UTC)Posts: 1,508Was thanked: 1285 time(s) in 750 post(s) 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. Russia ☭ forever Viacheslav N. Mezentsev
 uni #70 Posted : 19 July 2018 13:45:36(UTC) Rank: Advanced MemberGroups: Registered, Advanced MemberJoined: 10/11/2010(UTC)Posts: 1,508Was thanked: 1285 time(s) in 750 post(s) Updated. Skip intel ode assembly loading if Linux used. So in Linux only 2 functions available: rkfixed() and Rkadapt().Raspbian on RaspberryPi 3. Russia ☭ forever Viacheslav N. Mezentsev
 uni #71 Posted : 01 August 2018 19:12:03(UTC) Rank: Advanced MemberGroups: Registered, Advanced MemberJoined: 10/11/2010(UTC)Posts: 1,508Was thanked: 1285 time(s) in 750 post(s) Simple intel ode test 2. iode.test2.sm (23kb) downloaded 89 time(s). iode.test2.pdf (122kb) downloaded 72 time(s).Edited by user 24 December 2018 11:55:44(UTC)  | Reason: Not specified Russia ☭ forever Viacheslav N. Mezentsev 1 user thanked uni for this useful post. on 02/08/2018(UTC)
 uni #72 Posted : 03 December 2018 23:21:26(UTC) Rank: Advanced MemberGroups: Registered, Advanced MemberJoined: 10/11/2010(UTC)Posts: 1,508Was thanked: 1285 time(s) in 750 post(s) Updated. Fixed issue with zero point.ODE test 3. Something wrong with Rkadapt(). iode.test3.sm (25kb) downloaded 35 time(s). iode.test3.pdf (113kb) downloaded 34 time(s). Russia ☭ forever Viacheslav N. Mezentsev 1 user thanked uni for this useful post. on 04/12/2018(UTC)
 Razonar #73 Posted : 04 December 2018 05:32:02(UTC) Rank: Advanced MemberGroups: Registered Joined: 28/08/2014(UTC)Posts: 1,405Was thanked: 857 time(s) in 543 post(s) 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)  | Reason: Not specified
 Jean Giraud #74 Posted : 04 December 2018 07:40:00(UTC) Rank: GuestGroups: Registered Joined: 04/07/2015(UTC)Posts: 6,866Was thanked: 983 time(s) in 811 post(s) 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).
 Jean Giraud #75 Posted : 04 December 2018 07:43:31(UTC) Rank: GuestGroups: Registered Joined: 04/07/2015(UTC)Posts: 6,866Was thanked: 983 time(s) in 811 post(s) 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).
 Jean Giraud #76 Posted : 04 December 2018 15:55:44(UTC) Rank: GuestGroups: Registered Joined: 04/07/2015(UTC)Posts: 6,866Was thanked: 983 time(s) in 811 post(s) 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).
 Jean Giraud #77 Posted : 04 December 2018 16:17:01(UTC) Rank: GuestGroups: Registered Joined: 04/07/2015(UTC)Posts: 6,866Was thanked: 983 time(s) in 811 post(s) 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 sizeAs it looks Smath Rkadapt muffs the start,Try 34/35 => observe the result. iode.test3 Strip Rkadapt.sm (17kb) downloaded 32 time(s).
 Jean Giraud #78 Posted : 04 December 2018 16:31:24(UTC) Rank: GuestGroups: Registered Joined: 04/07/2015(UTC)Posts: 6,866Was thanked: 983 time(s) in 811 post(s) 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).
 Razonar #79 Posted : 04 December 2018 18:10:00(UTC) Rank: Advanced MemberGroups: Registered Joined: 28/08/2014(UTC)Posts: 1,405Was thanked: 857 time(s) in 543 post(s) 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 sizeHi. Probably, acc = (some tol) and s = minimun step size, in case that s = s/2 is too small.Best regards.Alvaro.
 Jean Giraud #80 Posted : 05 December 2018 21:34:53(UTC) Rank: GuestGroups: Registered Joined: 04/07/2015(UTC)Posts: 6,866Was thanked: 983 time(s) in 811 post(s) 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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