Spectral collocation solutions to multiparameter Mathieu's system

被引：12

作者：

Gheorghiu, C. I. ^{[1
]}

Hochstenbach, M. E. ^{[2
]}

Plestenjak, B. ^{[3
]}

Rommes, J. ^{[4
]}

机构：

[1] T Popoviciu Inst Numer Anal, POB 68, Cluj Napoca 3400 1, Romania

[2] Tech Univ Eindhoven, Dept Math & Comp Sci, NL-5600 MB Eindhoven, Netherlands

[3] Univ Ljubljana, Dept Math, SI-1000 Ljubljana, Slovenia

[4] NXP Semicond, Cent R&D, NL-5656 AE Eindhoven, Netherlands

来源：

APPLIED MATHEMATICS AND COMPUTATION | 2012年 / 218卷 / 24期

关键词：

Mathieu's system; Chebyshev collocation; Multiparameter eigenvalue problem; Jacobi-Davidson method; Tensor Rayleigh quotient iteration;

D O I：

10.1016/j.amc.2012.05.068

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

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. (C) 2012 Elsevier Inc. All rights reserved.

引用

页码：11990 / 12000

页数：11

共 29 条

[1] [Anonymous], 2000, SIAM
[2] [Anonymous], 1998, A Practical Guide to Pseudospectral Methods
[3] [Anonymous], LECT NOTES ENG
[4] [Anonymous], 2007, Spectral Methods for Differential Problems
[5] [Anonymous], IMPLEMENTATION BOUND
[6] Atkinson F., 1972, MULTIPARAMETER EIGEN
[7] Analytical and numerical solutions to an electrohydrodynamic stability problem
Dragomirescu, F. I.
Gheorghiu, C. I.
[J]. APPLIED MATHEMATICS AND COMPUTATION, 2010, 216 (12) : 3718 - 3727
[8] Finch S.R., 2008, MATHIEU EIGENVALUES
[9] Spectral methods in linear stability. Applications to thermal convection with variable gravity field
Gheorghiu, C. I.
Dragomirescu, Florica-Loana
[J]. APPLIED NUMERICAL MATHEMATICS, 2009, 59 (06) : 1290 - 1302
[10] Golub G. H., 1996, MATRIX COMPUTATIONS

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