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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 123 time(s).
iode.kinetic1.sm (8kb) downloaded 70 time(s).
iode.kinetic2.sm (15kb) downloaded 59 time(s).
iode.kinetic3.sm (15kb) downloaded 59 time(s).
iode.integrate.sm (11kb) downloaded 66 time(s).
iode.test1.sm (23kb) downloaded 69 time(s).
iode.test2.sm (23kb) downloaded 55 time(s).
iode.Amplitude detector.sm (21kb) downloaded 57 time(s).
Box_models.sm (101kb) downloaded 53 time(s).

iode.examples.pdf (417kb) downloaded 94 time(s).
iode.kinetic1.pdf (75kb) downloaded 57 time(s).
iode.kinetic2.pdf (91kb) downloaded 39 time(s).
iode.kinetic3.pdf (89kb) downloaded 43 time(s).
iode.integrate.pdf (89kb) downloaded 50 time(s).
iode.test1.pdf (117kb) downloaded 50 time(s).
iode.test2.pdf (122kb) downloaded 41 time(s).
iode.Amplitude detector.pdf (148kb) downloaded 44 time(s).
Box_models.pdf (146kb) downloaded 40 time(s).

Links:

1. Intel ODE Solver Library.

Edited by user 14 August 2019 23:28:14(UTC)  | Reason: Not specified

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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 Jean Giraud  
#2 Posted : 01 February 2019 04:35:35(UTC)
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Hello Viacheslav,
IMHO, your first example fails, it ignores Ao.

ODE_Lib.PNG
Offline uni  
#3 Posted : 01 February 2019 05:14:30(UTC)
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I didn't quite understand exactly what you mean.
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Offline Jean Giraud  
#4 Posted : 01 February 2019 15:15:08(UTC)
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Originally Posted by: uni Go to Quoted Post
I didn't quite understand exactly what you mean.


Just confusing between the variable of integration [A, X]
Even more confusing Ao. My maths are still Cartesian wrt
the variable of integration X.

Cheers ... Jean

ODE stiff.sm (40kb) downloaded 50 time(s).
Offline omorr  
#5 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 14 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  
#6 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 14 time(s).
Offline uni  
#7 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


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thanks 1 user thanked uni for this useful post.
on 11/07/2021(UTC)
Offline omorr  
#8 Posted : 11 July 2021 21:59:35(UTC)
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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!"
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