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Mathieu functions toolbox

Solve Mathieu equations
(1461 downloads for this version - 13007 downloads for all versions)
Details
Version
2.0
A more recent valid version with binaries for Scilab 5.2 exists: 3.0
Authors
R. Coisson, G. Vernizzi, XK. Yang, N. Strelkov
Michael Baudin
Owner Organization
Parma University - DIGITEO
Maintainers
Michael Baudin
Robert Coisson
Nikolay Strelkov
Category
License
Dependency
Creation Date
June 8, 2011
Source created on
Scilab 5.2.x
Binaries available on
Scilab 5.2.x:
Windows 64-bit Windows 32-bit Linux 64-bit Linux 32-bit MacOSX
Install command
--> atomsInstall("Mathieu")
Description
            This Mathieu Functions Toolbox is used to solve Mathieu function numerically.

The Mathieu equation is a second-order homogeneous linear differential equation

and appears in several different situations in Physics: electromagnetic or
elastic 
wave equations with elliptical boundary conditions as in waveguides
or resonators, the motion of particles in alternated-gradient
focussing or electromagnetic traps, the inverted pendulum,
parametric oscillators, the motion of a quantum particle in
a periodic potential, the eigenfunctions of the quantum pendulum, are just few
examples. 
Their solutions, known as Mathieu functions,
were first discussed by Mathieu in 1868 in the context of the
free oscillations of an elliptic membrane.
 
The toolbox has 8 demos. 
All demos can be acessed from "?->Scilab Demonstrations"


Features
--------
 * mathieu_cart2ell : Converts from cartesian to elliptical coordinates.
 * mathieu_ell2cart : Converts from elliptical to cartesian coordinates.
 * mathieu_ellipse : 3D plot of a mode with elliptical boundary conditions.
 * mathieu_elliptical : 3D plot of a mode with elliptical boundary conditions.
 * mathieu_expqa : Plot nu with respect to q and a.
 * mathieu_mathieu: Evaluates periodic Mathieu functions.
 * mathieu_mathieuS: Calculates solutions of Mathieu Equation.
 * mathieu_mathieuexp:  Evaluates the characteristic exponent.
 * mathieu_mathieuf: Evaluates characteristic values and expansion
coefficients.


Bibliography
------------
 * R. Coïsson, G. Vernizzi and X.K. Yang, "Mathieu functions and numerical
solutions of the Mathieu equation", IEEE Proceedings of OSSC2009, online at http://www.fis.unipr.it/~coisson/Mathieu.pdf

 * N.W. McLachlan, Theory and Application of Mathieu Functions, Oxford Univ.
Press, 1947
 * J. C. Gutiérrez-Vega, R. M. Rodríguez-Dagnino, M. A. Meneses-Nava, and S.
Chávez-Cerda, "Mathieu functions, a visual approach", American Journal of
Physics, 71 (233), 233-242. An introduction to applications, online at http://www.df.uba.ar/users/sgil/physics_paper_doc/papers_phys/modern/matheiu0.pdf
            
Files (2)
[53.74 kB]
Source code archive

[88.56 kB]
OS-independent binary for Scilab 5.2.x
Binary version
Automatically generated by the ATOMS compilation chain

News (0)
Comments (2)     Leave a comment 
Comment from Michael Baudin -- June 9, 2011, 04:00:22 PM    
The version 2.0 is correctly packaged. On Windows 32 bits:

-->atomsTest("Mathieu")
   TMPDIR = C:\Users\baudin\AppData\Local\Temp\SCI_TMP_3520_

   001/007 - [SCI\contrib\Mathieu\2.0-1] cart2ell..................passed 
   002/007 - [SCI\contrib\Mathieu\2.0-1] ell2cart..................passed 
   003/007 - [SCI\contrib\Mathieu\2.0-1] ellipse...................passed 
   004/007 - [SCI\contrib\Mathieu\2.0-1] elliptical................passed 
   005/007 - [SCI\contrib\Mathieu\2.0-1] mathieu...................passed 
   006/007 - [SCI\contrib\Mathieu\2.0-1] mathieuexp................passed 
   007/007 - [SCI\contrib\Mathieu\2.0-1] mathieuf..................passed 

Regards,

Michaël Baudin
Answer from Nikolay Strelkov -- June 9, 2011, 04:12:18 PM    
> The version 2.0 is correctly packaged. On Windows 32 bits:
> 
> -->atomsTest("Mathieu")
>    TMPDIR = C:\Users\baudin\AppData\Local\Temp\SCI_TMP_3520_
> 
>    001/007 - [SCI\contrib\Mathieu\2.0-1] cart2ell..................passed 
>    002/007 - [SCI\contrib\Mathieu\2.0-1] ell2cart..................passed 
>    003/007 - [SCI\contrib\Mathieu\2.0-1] ellipse...................passed 
>    004/007 - [SCI\contrib\Mathieu\2.0-1] elliptical................passed 
>    005/007 - [SCI\contrib\Mathieu\2.0-1] mathieu...................passed 
>    006/007 - [SCI\contrib\Mathieu\2.0-1] mathieuexp................passed 
>    007/007 - [SCI\contrib\Mathieu\2.0-1] mathieuf..................passed 
> 
> Regards,
> 
> Michaël Baudin

Thank you, Michaël!

Same on Linux 32, 64 bits.
Answer from Nikolay Strelkov -- June 9, 2011, 06:30:28 PM    
Same on Windows 64 bits.
Comment from Michael Baudin -- June 9, 2011, 04:01:19 PM    
Here is the changelog for the version 2.0.


Mathieu Functions Toolbox (v2.0)
 * 23/05/2011: Source code uploaded to Scilab 
   Forge: http://forge.scilab.org/index.php/p/mathieu/
 * 16/05/2011: Changed directory structure as it required 
   by ATOMS packaging system. Removed temporary files.
 * 16/05/2011: Fixed 'error 15' in mathieuf example.
 * MB: Fixed the startup script name.
 * MB: Fixed the messages in the console.
 * MB: Fixed the encoding of the scripts, indented them.
 * MB: Updated the readme, the changelog.
 * MB: Simplified the descriptions of the functions.
 * MB: Added a description for the invellip function.
 * 03/06/2011:
 * NS: Renamed invellip to cart2ell
 * NS: Renamed all functions into mathieu_* to avoid name conflicts 
   (cart2ell->mathieu_cart2ell, 
   ell2cart->mathieu_ell2cart, 
   ellipse->mathieu_ellipse,
   elliptical->mathieu_elliptical,
   expqa->mathieu_expqa,
   mathieu->mathieu_mathieu, 
   mathieuexp->mathieu_mathieuexp, 
   mathieuf->mathieu_mathieuf, 
   mathieuS->mathieu_mathieuS), 
   updated help pages
 * MB: created unit tests.
 * MB: removed unnecessary calls to ieee and mode functions.
 * MB: Added licence headers to the macros.
 * NS: removed remained unnecessary calls to ieee and mode functions.
 * NS: changed TOOLBOX_TITLE
 * NS: fixed 'error 15' mathieuf.tst unit test.
 * MB: Fixed formatting of help pages.
 * MB: Added an example in mathieu_cart2ell.xml.
 * MB: Created an overview help page.
 * MB: Added licence header into mathieu_cart2ell.
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