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OSLO - Open Solving Library for ODEs  Functions list: RK547M(5), GearBDF(5)RK547M(init, x1, x2, intvls, D) Implementation of Runge-Kutta algoritm with per-point accurancy control from Dormand and Prince article. GearBDF(init, x1, x2, intvls, D) Implementation of Gear's BDF method with dynamically changed step size and order. Order changes between 1 and 3. Arguments: - init is either a vector of n real initial values, where n is the number of unknowns (or a single scalar initial value, in the case of a single ODE). - x1 and x2 are real, scalar endpoints of the interval over which the solution to the ODE(s) is evaluated. Initial values in init are the values of the ODE function(s) evaluated at x1. - intvls is the integer number of discretization intervals used to interpolate the solution function. The number of solution points is the number of intervals + 1. - D is a vector function of the form D(x,y) specifying the right-hand side of the system Options: - AbsTol - absolute tolerance parameter, default value 10⁻⁷. - RelTol - relative tolerance parameter, default value 10⁻⁴. - MaxStep - maximal step value, default value x2-x1. Links: 1. Open Solving Library for ODEs. 2. OSLO User Guide (pdf). Open Solving Library for ODEs (OSLO) 1.0 User Guide.pdf (1,174kb) downloaded 35 time(s). oslo.integrate.sm (11kb) downloaded 62 time(s). oslo.kinetic1.sm (8kb) downloaded 49 time(s). oslo.kinetic2.sm (12kb) downloaded 52 time(s). oslo.kinetic3.sm (12kb) downloaded 48 time(s). oslo.test1.sm (16kb) downloaded 42 time(s). oslo.test2.sm (16kb) downloaded 45 time(s). oslo.Amplitude detector.sm (21kb) downloaded 45 time(s). oslo.integrate.pdf (89kb) downloaded 51 time(s). oslo.kinetic1.pdf (76kb) downloaded 45 time(s). oslo.kinetic2.pdf (92kb) downloaded 44 time(s). oslo.kinetic3.pdf (86kb) downloaded 41 time(s). oslo.test1.pdf (100kb) downloaded 40 time(s). oslo.test2.pdf (102kb) downloaded 41 time(s). oslo.Amplitude detector.pdf (150kb) downloaded 44 time(s).See also:● Mathcad Toolbox● Intel ODE Solver Library● DotNumerics● SADEL● Matlab C++ Math Library● lsoda● GNU Scientific Library (GSL)Edited by user 06 July 2022 14:51:03(UTC)
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Russia ☭ forever (git.io/vOZo0) Viacheslav N. Mezentsev |
 5 users thanked uni for this useful post.
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on 19/01/2019(UTC), on 19/01/2019(UTC), on 19/01/2019(UTC), on 19/01/2019(UTC), on 20/01/2019(UTC)
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Hello uni, Thank you for some more ODE solvers. However, I could not resist to mention my favorite db_GearsBDF() which can escape the problem when y2 approaches zero. I mentioned this stiff example long time ago and you were using it often (kinetic2.sm example here). Unfortunately, it seams GearBDF() from this plugin can not overcome zero values and gets into the negative ones like most of the solvers.  Regards, Radovan |
When Sisyphus climbed to the top of a hill, they said: "Wrong boulder!" |
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Yes, weak solvers. There are some settings there, but I was not able to select them correctly for this task. Another strange problem with accuracy. Unlike other solvers, a smaller step is needed here. In general, there are questions to the developers (Microsoft Research and Moscow State University). Not only dn_GearsBDF() can solve your task. Some other solvers have also achieved success. Still looking for the best. Not all solvers are still implemented, the test suite is also still small. |
Russia ☭ forever (git.io/vOZo0) Viacheslav N. Mezentsev |
 3 users thanked uni for this useful post.
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on 19/01/2019(UTC), on 19/01/2019(UTC), on 19/01/2019(UTC)
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Originally Posted by: uni  ... the test suite is also still small. Hi Viacheslav. Maybe you're interested in check this matlab ode's: http://people.sc.fsu.edu...c/test_ode/test_ode.html . At the end, there are also png images for the plots. Best regards. Alvaro.
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Russia ☭ forever (git.io/vOZo0) Viacheslav N. Mezentsev |
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Originally Posted by: uni  In this link it was mentioned about the book and packages made in R (Karline Soetaert et al). I was exposing my students to the R and some of their packages (deSolve, bvpSolve, rootSolve etc.) for few years now. I am really impressed by them. There are solvers for IVP, BVP, DAE, PDE etc. All my credits to the authors and their efforts. Surprisingly, there are quite a lot numerical packages in R which is considered to be mainly a statistical environment. Regards, Radovan |
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Originally Posted by: omorr  In this link it was mentioned about the book and packages made in R (Karline Soetaert et al). I was exposing my students to the R and some of their packages (deSolve, bvpSolve, rootSolve etc.) for few years now. I am really impressed by them. There are solvers for IVP, BVP, DAE, PDE etc. All my credits to the authors and their efforts. Surprisingly, there are quite a lot numerical packages in R which is considered to be mainly a statistical environment. Can't be more right Radovan: for using R, better be an R manAll those solvers fall in the category Lagrangian Methods quite evolved since CAS Soon, there will be as many dedicated ODE solvers as they will be proved for Physicals system to solve. dn_GearsBDF is a good companion for stiff systems, and hyper fast [see comparison attached]. Jean ODE HIRES.sm (58kb) downloaded 29 time(s).
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... Legendre_Radau updated wrt local definition ODE HIRES.sm (68kb) downloaded 32 time(s).
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 1 user thanked Jean Giraud for this useful post.
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Originally Posted by: Jean Giraud  You are welcome Jean, and thank you. There is another one by uni - lsoda. Regards, Radovan |
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Originally Posted by: omorr  You are welcome Jean, and thank you. There is another one by uni - lsoda. Thanks Radovan, As it looks, the previous 8 ODE from Viacheslav are all Isoda. Do you feel comfortable to code Smath ? An all version(s) compatible will enhance the native tiny Smath. Naturally, Smath does not solve the "Pulse". Does not recognize F(t). Cheers ... Jean
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 Plugin updated. Changes: - added support for ODE systems in mathematical form; - default value for MaxStep changed from h/2 to xmax-xmin; - refactored. |
Russia ☭ forever (git.io/vOZo0) Viacheslav N. Mezentsev |
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 Plugin updated. Changes: - solution restructured; - converting the task for the ODE solver to the numerical form is now performed through the Mathcad Toolbox plugin (to avoid code duplication), so it must be installed; - refactored. Solvers that support mathematical notation now reuse code from the Mathcad Toolbox plugin. Now there is no need to recompile every such plugin. |
Russia ☭ forever (git.io/vOZo0) Viacheslav N. Mezentsev |
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