Correction of Sturm-Liouville eigenvalue estimates

Paine, J.

doi:10.1090/S0025-5718-1982-0669636-4

Correction of Sturm-Liouville eigenvalue estimates
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Math. Comp. 39 (1982), 415-420 Request permission

Correction: Math. Comp. 39 (1982), 415-420.
Original Article: Math. Comp. 39 (1982), 415-420.

Abstract:

The error in the Sturm-Liouville eigenvalue estimates obtained by replacing the coefficient function with a piecewise constant interpolate is not uniform. In this paper we present a method for correcting these estimates to obtain a uniform approximation of all eigenvalues.

References

Garrett Birkhoff, C. de Boor, B. Swartz, and B. Wendroff, Rayleigh-Ritz approximation by piecewise cubic polynomials, SIAM J. Numer. Anal. 3 (1966), 188–203. MR 203926, DOI 10.1137/0703015

J. Comput. Phys.

R. Courant and D. Hilbert, Methods of mathematical physics. Vol. I, Interscience Publishers, Inc., New York, N.Y., 1953. MR 0065391
B. E. Hubbard, Bounds for eigenvalues of the Sturm-Liouville problem by finite difference methods, Arch. Rational Mech. Anal. 10 (1962), 171–179. MR 145670, DOI 10.1007/BF00281184

J. Comput. Phys.

Herbert B. Keller, Numerical methods for two-point boundary-value problems, Blaisdell Publishing Co. [Ginn and Co.], Waltham, Mass.-Toronto, Ont.-London, 1968. MR 0230476

J. Austal. Math. Soc. Ser. B

Steven Pruess, Estimating the eigenvalues of Sturm-Liouville problems by approximating the differential equation, SIAM J. Numer. Anal. 10 (1973), 55–68. MR 327048, DOI 10.1137/0710008