Remote Access Mathematics of Computation
Green Open Access

Mathematics of Computation

ISSN 1088-6842(online) ISSN 0025-5718(print)

 
 

 

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
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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 [Enhancements On Off] (What's this?)

  • [1] G. Birkhoff, C. de Boor, B. Swartz & B. Wendroff, "Rayleigh-Ritz approximation by piecewise polynomials," SIAM J. Numer. Anal., v. 3, 1966, pp. 188-203. MR 0203926 (34:3773)
  • [2] 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.
  • [3] R. Courant & D. Hilbert, Methods of Mathematical Physics, Vol. I, Interscience, New York, 1953. MR 0065391 (16:426a)
  • [4] B. Hubbard, "Bounds for eigenvalues of the Sturm-Liouville problem by finite difference methods," Arch. Rational Mech. Anal., v. 10, 1962, pp. 171-179. MR 0145670 (26:3199)
  • [5] L. Gr. Ixaru, "The error analysis of the algebraic method for solving the Schrödinger equation," J. Comput. Phys., v. 9, 1972, pp. 159-163.
  • [6] H. B. Keller, Numerical Methods for Two-point Boundary Value Problems, Blaisdell, Waltham, Mass., 1968. MR 0230476 (37:6038)
  • [7] 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.
  • [8] S. Pruess, "Estimating the eigenvalues of Sturm-Liouville problems by approximating the differential equation," SIAM J. Numer. Anal., v. 10, 1973, pp. 55-68. MR 0327048 (48:5390)

Similar Articles

Retrieve articles in Mathematics of Computation with MSC: 65L15

Retrieve articles in all journals with MSC: 65L15


Additional Information

DOI: https://doi.org/10.1090/S0025-5718-1982-0669636-4
Article copyright: © Copyright 1982 American Mathematical Society

American Mathematical Society