[1] Huang Bin, Hu Weiqun,. Finite element method of the eigenvaluesof Sturm-Liouville’s problem [J]. Journal of Southeast University (English Edition), 2003, 19 (4): 437-442. [doi:10.3969/j.issn.1003-7985.2003.04.028]

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Finite element method of the eigenvaluesof Sturm-Liouville’s problem()

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Journal of Southeast University (English Edition)[ISSN:1003-7985/CN:32-1325/N]

Volumn:

19

Issue:

2003 4

Page:

437-442

Research Field:

Mathematics, Physics, Mechanics

Publishing date:

2003-12-30

Info

Title:

Finite element method of the eigenvaluesof Sturm-Liouville’s problem

Author(s):

Huang Bin¹;  Hu Weiqun²

¹Department of Mechatronic Engineering, Jinling Institute of Technology, Nanjing 210038, China
²Information College, Nanjing Forestry University, Nanjing 210037, China

Keywords:

Sturm-Liouville’s problem;  eigenvalue;  eigenfunction;  finite element method

PACS:

O175.1

DOI:

10.3969/j.issn.1003-7985.2003.04.028

Abstract:

This paper considers the finite element method of the approximate value of eigenvalues of Sturm-Liouville’s problem. The proof of our main result is based on the variational method. Linear interpolating functions are made by interpolation method, the problem of the approximate value of eigenvalues becomes the calculation of eigenvlaues of a matrix. Then the finite element method of the approximate value of the eigenvalues is obtained, and accuracy of(n-1)-th approximate value is estimated by n-th approximate value. When n is increased, the accuracy of eigenvalue λ_k is increased. When n is appropriately selected, the accuracy of λ_k we need is obtained. This finite element method is significant both in applications and in theory.

References:

[1] Hile G N, Protter M H. Inequalities for eigenvalue of the Laplacian [J]. Indiana Univ Math J, 1980, 29(4): 523-538.
[2] Hile G N, Yeh R Z. Inequalities for eigenvalue of the biharmonic operator [J]. Pacific J Math, 1984, 112(1): 115-133.
[3] Chen Z C, Qian C L. Estimates for discrete spectrum of Laplacian operator with any order [J]. J China Univ Sci Tech, 1990, 20(3):259-265.
[4] Protter M H. Can one hear the shape of a drum?[J]. SIAM Rev, 1987, 29(2):185-197.
[5] Zhen W G, Qian C L. Estimates for eigenvalue of Sturm-Liouville’s problem [J]. J Math Tech, 1992, 8(1):28-32.(in Chinese)
[6] Huang Bin. One computational method of the eigenvalues of the horizontal across vibration problem of beam [J]. Journal of Southeast University(English Edition), 2002, 18(4):277-282.

Memo

Memo:

Biography: Huang Bin(1958—), male, lecturer, binhuang@public1.ptt.js.cn.

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