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Offline uni  
#1 Posted : 31 January 2019 23:48:55(UTC)
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Intel ODE Solver Library

SMath Studio compatibility SMath Viewer compatibility mono compatibility Platform Extension page Sources


Functions list: rkm9st(5), mk52lfn(5), mk52lfa(5), rkm9mkn(5), rkm9mka(5).


rkm9st(init, x1, x2, intvls, D) A specialized routine for solving non-stiff and middle-stiff ODE systems using the explicit method, which is based on the 4th order Merson’s method and the 1st order multistage method of up to and including 9 stages with stability control.

mk52lfn(init, x1, x2, intvls, D) A specialized routine for solving stiff ODE systems using the implicit method based on L-stable (5,2)-method with the numerical Jacobi matrix, which is computed by the routine.

mk52lfa(init, x1, x2, intvls, D) A specialized routine for solving stiff ODE systems using the implicit method based on L-stable (5,2)-method with numerical or analytical computation of the Jacobi matrix. The user must provide a routine for this computation.

rkm9mkn(init, x1, x2, intvls, D) A specialized routine for solving ODE systems with a variable or a priori unknown stiffness; automatically chooses the explicit or implicit scheme in every step and computes the numerical Jacobi matrix when necessary.

rkm9mka(init, x1, x2, intvls, D) A specialized routine for solving ODE systems with a variable or a priori unknown stiffness; automatically chooses the explicit or implicit scheme in every step. The user must provide a routine for numerical or analytical computation of the Jacobi matrix.


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



iode.examples.sm (205kb) downloaded 164 time(s).
iode.kinetic1.sm (8kb) downloaded 96 time(s).
iode.kinetic2.sm (15kb) downloaded 76 time(s).
iode.kinetic3.sm (15kb) downloaded 77 time(s).
iode.integrate.sm (11kb) downloaded 86 time(s).
iode.test1.sm (23kb) downloaded 89 time(s).
iode.test2.sm (23kb) downloaded 74 time(s).
iode.Amplitude detector.sm (21kb) downloaded 81 time(s).
Box_models.sm (101kb) downloaded 63 time(s).

iode.examples.pdf (417kb) downloaded 131 time(s).
iode.kinetic1.pdf (75kb) downloaded 77 time(s).
iode.kinetic2.pdf (91kb) downloaded 55 time(s).
iode.kinetic3.pdf (89kb) downloaded 59 time(s).
iode.integrate.pdf (89kb) downloaded 66 time(s).
iode.test1.pdf (117kb) downloaded 65 time(s).
iode.test2.pdf (122kb) downloaded 59 time(s).
iode.Amplitude detector.pdf (148kb) downloaded 63 time(s).
Box_models.pdf (146kb) downloaded 48 time(s).

See also:

Mathcad Toolbox
DotNumerics
SADEL
Matlab C++ Math Library
OSLO
lsoda
GNU Scientific Library (GSL)

Edited by user 12 December 2021 23:22:53(UTC)  | Reason: Not specified

Russia ☭ forever
Viacheslav N. Mezentsev
thanks 3 users thanked uni for this useful post.
on 01/02/2019(UTC),  on 01/02/2019(UTC),  on 01/02/2019(UTC)
Offline omorr  
#2 Posted : 11 July 2021 15:47:22(UTC)
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Hmm...even dn_GearsBDF() will go nuts for this example.

Just for the record...

iode.Amplitude detector-1.sm.png
iode.Amplitude detector-1.sm (20kb) downloaded 17 time(s).

EDIT: mk52lfa() and mk52lfn() will also perform well here

Edited by user 11 July 2021 16:00:40(UTC)  | Reason: Not specified

When Sisyphus climbed to the top of a hill, they said: "Wrong boulder!"
Offline Jean Giraud  
#3 Posted : 11 July 2021 16:15:24(UTC)
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Originally Posted by: omorr Go to Quoted Post
Hmm...even dn_GearsBDF() will go nuts for this example.

From recollection,NONE ODE solve that one.
Cheers ... Jean.

ODE rkfixed Pulse Pitfall.sm (38kb) downloaded 18 time(s).
Offline uni  
#4 Posted : 11 July 2021 18:20:01(UTC)
uni


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Originally Posted by: omorr Go to Quoted Post
Hmm...even dn_GearsBDF() will go nuts for this example.

A little help is needed here

2021-07-11_20-18-09.png


Russia ☭ forever
Viacheslav N. Mezentsev
thanks 1 user thanked uni for this useful post.
on 11/07/2021(UTC)
Offline omorr  
#5 Posted : 11 July 2021 21:59:35(UTC)
omorr


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I should have guessed that Good . Thank you.
When Sisyphus climbed to the top of a hill, they said: "Wrong boulder!"
Offline uni  
#6 Posted : 09 December 2021 22:12:56(UTC)
uni


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Was thanked: 1151 time(s) in 664 post(s)
SMath Studio compatibility

Plugin updated.

Changes:

- added support for ODE systems in mathematical form;
- refactored.
Russia ☭ forever
Viacheslav N. Mezentsev
thanks 2 users thanked uni for this useful post.
on 09/12/2021(UTC),  on 10/12/2021(UTC)
Offline uni  
#7 Posted : 20 December 2021 22:17:42(UTC)
uni


Rank: Advanced Member

Groups: Registered, Advanced Member
Joined: 10/11/2010(UTC)
Posts: 1,317
Man
Russian Federation

Was thanked: 1151 time(s) in 664 post(s)
SMath Studio compatibility

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
Viacheslav N. Mezentsev
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