<< mathieu_mathieuexp Mathieu mathieu_membrane_mode >>

Mathieu >> Mathieu > mathieu_mathieuf

mathieu_mathieuf

Evaluates characteristic values and expansion coefficients.

Calling Sequence

[ab,c] = mathieu_mathieuf(q,dimM)

Parameters

ab

the characteristic values with ordering and , for q complex, the ordering is not well-defined.

c

coefficients of expansions of Periodic Mathieu Functions ce,se,Ce,Se,Fey,Gey,Fek,Gek. c is a matrix: all values of n from -dimM to dimM are calculated.

q

the parameter(real) of the confocal ellipse family (q=0: circle)

dimM

matrix dimension in the calculation (default dimM=10)

Description

Mathieu_mathieuf evaluates characteristic values and expansion coefficients of periodic solutions of the differential equation

(Mathieu equation)

or to solutions of

(Modified Mathieu equation)

Examples

// Eigenvalues (imaginary vs. real part) for complex values of q
// (see fig. 7 of [1])
for t=0.1:0.2:15
    plot( real(2+mathieu_mathieuf(2+t*%i, 6)), imag(mathieu_mathieuf(2+t*%i, 6)), '.');
end
xgrid;
xtitle('Eigenvalues (imaginary vs. real part) for complex values of q', '$Re[\lambda]$', '$Im[\lambda]$');

See Also

Used Functions

besselj

Authors

R.Coisson and G. Vernizzi, Parma University

X. K. Yang

N. O. Strelkov, NRU MPEI

2011 - DIGITEO - Michael Baudin

Bibliography

1. 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).


Report an issue
<< mathieu_mathieuexp Mathieu mathieu_membrane_mode >>