# Spectral collocation solutions to multiparameter Mathieu’s system

## Abstract

Our main aim is the accurate computation of a large number of specified eigenvalues and eigenvectors of Mathieu’s system as a multiparameter eigenvalue problem (MEP). The reduced wave equation, for small deflections, is solved directly without approximations introduced by the classical Mathieu functions. We show how for moderate values of the cut-off collocation parameter the QR algorithm and the Arnoldi method may be applied successfully, while for larger values the Jacobi–Davidson method is the method of choice with respect to convergence, accuracy and memory usage.

## Authors

Călin-Ioan Gheorghiu
(Tiberiu Popoviciu Institute of Numerical Analysis, Romanian Academy)

M. E. Hochstenbach
(Department of Mathematics and Computer Science, TU Eindhoven)

B. Plestenjak
(Department of Mathematics, University of Ljubljana)

J. Rommes
(NXP Semiconductors, The Netherlands)

## Keywords

Mathieu’s system; Chebyshev collocation; multiparameter eigenvalue problem; Jacobi–Davidson method; tensor Rayleigh quotient iteration.

### References

See the expanding block below.

## Cite this papaer as

C.I. Gheorghiu, M.E. Hochstenbach, B. Plestenjak, J. Rommes, Spectral collocation solutions to multiparameter Mathieu’s system, Appl. Math. Comput., 218 (2012) 11990-12000.
doi: 10.1016/j.amc.2012.05.068

## PDF

http://www.win.tue.nl/~hochsten/pdf/mathieu.pdf

Elsevier

0096-3003