Correction of finite element eigenvalues for problems with natural or periodic boundary conditions

Alan L. Andrew

doi:10.1007/bf01934090

journal article Jun 01, 1988

Correction of finite element eigenvalues for problems with natural or periodic boundary conditions

Alan L. Andrew

BIT Numerical Mathematics Vol. 28 No. 2 pp. 254-269 · Springer Science and Business Media LLC

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References

18

[1]

R. S. Anderssen and F. R. De Hoog,On the correction of finite difference eigenvalue approximations for Sturm-Liouville problems with general boundary conditions, Tech. Rep. CMA-RO5-82, Centre for Math. Analysis, Australian National Univ., 1982.

[2]

R. S. Anderssen and F. R. De Hoog,On the correction of finite difference eigenvalue approximations for Sturm-Liouville problems with general boundary conditions, BIT 24 (1984), 401–412. 10.1007/bf01934900

[3]

A. L. Andrew,Numerical solution of eigenvalue problems for ordinary differential equations, Computational Techniques and Applications: CTAC-83, J. Noye and C. Fletcher, eds., North-Holland, Amsterdam, 1984, 841–852.

[4]

A. L. Andrew,Asymptotic correction of finite difference eigenvalues, Computational Techniques and Applications: CTAC-85, J. Noye and R. May, eds., North-Holland, Amsterdam 1986, 333–341.

[5]

A. L. Andrew and J. W. Paine,Correction of Numerov's eigenvalue estimates, Numer. Math. 47 (1985), 289–300. 10.1007/bf01389712

[6]

A. L. Andrew and J. W. Paine,Correction of finite element estimates for Sturm-Liouville eigenvalues, Numer. Math. 50 (1986), 205–215. 10.1007/bf01390430

[7]

F. Chatelin,Spectral Approximation of Linear Operators. Academic Press, New York, 1983.

[8]

M. S. P. Eastham,The Spectral Theory of Periodic Differential Equations. Scottish Academic Press, Edinburgh, 1973.

[9]

D. J. Evans,Numerical solution of the Sturm-Liouville problem with periodic boundary conditions, Lecture Notes in Math. 228, Springer, Berlin 1971, 277–289. 10.1007/bfb0069462

[10]

H. Hochstadt,Asymptotic estimates for the Sturm-Liouville spectrum, Commun. Pure Appl. Math. 14 (1961), 749–764. 10.1002/cpa.3160140408

[11]

H. Hochstadt and W. Goldberg,On the integrability of Hill's equations with finite band spectra, J. Math. Anal. Appl. 94 (1983), 366–376. 10.1016/0022-247x(83)90069-0

[12]

J. Paine,A numerical method for the inverse Sturm-Liouville problem, SIAM J. Sci. Stat. Comput. 5 (1984), 149–156. 10.1137/0905011

[13]

J. W. Paine, Unpublished numerical results, 1985.

[14]

J. W. Paine, F. R. De Hoog and R. S. Anderssen,On the correction of finite difference eigenvalue approximations for Sturm-Liouville problems, Computing 26 (1981), 123–139. 10.1007/bf02241779

[15]

M. Porter and E. L. Reiss,A numerical method for ocean-acoustic normal modes, J. Acoust. Soc. Amer. 76 (1984), 244–252. 10.1121/1.391101

[16]

P. Rabinowitz,The convergence of interpolatory product integration rules, BIT 26 (1986), 131–134. 10.1007/bf01939370

[17]

G. Strang and G. J. Fix,An Analysis of the Finite Element Method, Prentice-Hall, Englewood Cliffs, 1973.

[18]

J. H. Wilkinson,The Algebraic Eigenvalue Problem, Clarendon Press, Oxford, 1965.

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A modified difference scheme for periodic and semiperiodic Sturm-Liouville problems

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Details

Published: Jun 01, 1988
Vol/Issue: 28(2)
Pages: 254-269
License: View

Authors

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Alan L. Andrew

Cite This Article

Alan L. Andrew (1988). Correction of finite element eigenvalues for problems with natural or periodic boundary conditions. BIT Numerical Mathematics, 28(2), 254-269. https://doi.org/10.1007/bf01934090

Correction of finite element eigenvalues for problems with natural or periodic boundary conditions

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