Intel ODE Solver Library

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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 (204.21 KiB) downloaded 1936 time(s).
iode.kinetic1.sm (7.75 KiB) downloaded 1850 time(s).
iode.kinetic2.sm (14.4 KiB) downloaded 1742 time(s).
iode.kinetic3.sm (14.08 KiB) downloaded 6655 time(s).
iode.integrate.sm (10.57 KiB) downloaded 6663 time(s).
iode.test1.sm (22.49 KiB) downloaded 1740 time(s).
iode.test2.sm (22.5 KiB) downloaded 1856 time(s).
iode.Amplitude detector.sm (20.18 KiB) downloaded 1807 time(s).
Box_models.sm (100.18 KiB) downloaded 6575 time(s).

iode.examples.pdf (416.34 KiB) downloaded 1048 time(s).
iode.kinetic1.pdf (74.06 KiB) downloaded 888 time(s).
iode.kinetic2.pdf (90.4 KiB) downloaded 859 time(s).
iode.kinetic3.pdf (88.45 KiB) downloaded 840 time(s).
iode.integrate.pdf (88.91 KiB) downloaded 971 time(s).
iode.test1.pdf (116.24 KiB) downloaded 912 time(s).
iode.test2.pdf (121.64 KiB) downloaded 860 time(s).
iode.Amplitude detector.pdf (147.71 KiB) downloaded 960 time(s).
Box_models.pdf (145.32 KiB) downloaded 1002 time(s).

Documents:

Intel ODE Solver Library Reference Manual (2018).pdf (239.74 KiB) downloaded 1024 time(s).

See also:

● [topic=726]Mathcad Toolbox[/topic]
● [topic=1918]DotNumerics[/topic]
● [topic=13809]SADEL[/topic]
● [topic=1970]Matlab C++ Math Library[/topic]
● [topic=17063]OSLO[/topic]
● [topic=17067]lsoda[/topic]
● [topic=1997]GNU Scientific Library (GSL)[/topic]

Hmm...even dn_GearsBDF() will go nuts for this example.

Just for the record...


iode.Amplitude detector-1.sm (19.9 KiB) downloaded 3880 time(s).

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

Wrote

Hmm...even dn_GearsBDF() will go nuts for this example.

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

ODE rkfixed Pulse Pitfall.sm (37.2 KiB) downloaded 1559 time(s).

Wrote

Hmm...even dn_GearsBDF() will go nuts for this example.

A little help is needed here

I should have guessed that . Thank you.

Plugin updated.

Changes:

- added support for ODE systems in mathematical form;
- refactored.

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.