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Correction of Sturm-Liouville eigenvalue estimates


Author: J. Paine
Journal: Math. Comp. 39 (1982), 415-420
MSC: Primary 65L15
DOI: https://doi.org/10.1090/S0025-5718-1982-0669636-4
Correction: Math. Comp. 39 (1982), 415-420.
Original Article: Math. Comp. 39 (1982), 415-420.
MathSciNet review: 669636
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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.


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  • 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 https://doi.org/10.1137/0703015
  • J. Canosa & R. Gomes de Oliveira, "A new method for the solution of the Schrödinger equation," J. Comput. Phys., v. 5, 1970, pp. 188-207.
  • 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 https://doi.org/10.1007/BF00281184
  • L. Gr. Ixaru, "The error analysis of the algebraic method for solving the Schrödinger equation," J. Comput. Phys., v. 9, 1972, pp. 159-163.
  • 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. W. Paine & F. R. de Hoog, "Uniform estimation of the eigenvalues of Sturm-Liouville problems," J. Austal. Math. Soc. Ser. B, v. 21, 1980, pp. 356-383.
  • 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 https://doi.org/10.1137/0710008

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Article copyright: © Copyright 1982 American Mathematical Society