OSLO - Open Solving Library for ODEs

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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 29 time(s).

oslo.integrate.sm (11kb) downloaded 57 time(s).
oslo.kinetic1.sm (8kb) downloaded 46 time(s).
oslo.kinetic2.sm (12kb) downloaded 49 time(s).
oslo.kinetic3.sm (12kb) downloaded 45 time(s).
oslo.test1.sm (16kb) downloaded 39 time(s).
oslo.test2.sm (16kb) downloaded 42 time(s).
oslo.Amplitude detector.sm (21kb) downloaded 42 time(s).

oslo.integrate.pdf (89kb) downloaded 48 time(s).
oslo.kinetic1.pdf (76kb) downloaded 42 time(s).
oslo.kinetic2.pdf (92kb) downloaded 41 time(s).
oslo.kinetic3.pdf (86kb) downloaded 38 time(s).
oslo.test1.pdf (100kb) downloaded 37 time(s).
oslo.test2.pdf (102kb) downloaded 38 time(s).
oslo.Amplitude detector.pdf (150kb) downloaded 41 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)  | Reason: Not specified

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.

And another one: TEST SET FOR IVP SOLVERS.

Can't be more right Radovan: for using R, better be an R man
All 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 26 time(s).

... thanks Radovan for the undocumented

ODE GearsBDF Undocumented.sm (10kb) downloaded 40 time(s).

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

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.