Collocation approximation to eigenvalues of an ordinary differential equation: numerical illustrations
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- by Carl de Boor and Blair Swartz PDF
- Math. Comp. 36 (1981), 1-19 Request permission
Abstract:
We display the numerical results associated with the collocation of three eigenvalue problems using from one to four Gauss points per partition interval in order to document the sharpness of the error bounds we have previously obtained. The ordinary differential operators involved are real with constant coefficients; two of the problems have an eigenvalue whose ascent exceeds one. We propose an explanation for the observed manner in which a set of simple approximate eigenvalues can approach a single multiple eigenvalue.References
- Carl de Boor, A practical guide to splines, Applied Mathematical Sciences, vol. 27, Springer-Verlag, New York-Berlin, 1978. MR 507062
- Carl de Boor and Blâir Swartz, Collocation at Gaussian points, SIAM J. Numer. Anal. 10 (1973), 582–606. MR 373328, DOI 10.1137/0710052
- Carl de Boor and Blair Swartz, Comments on: “A comparison of global methods for linear two-point boundary value problems” (Math. Comp. 29 (1975), no. 132, 1007–1019) by R. D. Russell and J. M. Varah, Math. Comp. 31 (1977), no. 140, 916–921. MR 501939, DOI 10.1090/S0025-5718-1977-0501939-4
- Carl de Boor and Blair Swartz, Collocation approximation to eigenvalues of an ordinary differential equation: the principle of the thing, Math. Comp. 35 (1980), no. 151, 679–694. MR 572849, DOI 10.1090/S0025-5718-1980-0572849-1
- Earl A. Coddington and Norman Levinson, Theory of ordinary differential equations, McGraw-Hill Book Co., Inc., New York-Toronto-London, 1955. MR 0069338 S. D. Conte & C. de Boor, Elementary Numerical Analysis, 2nd ed., McGraw-Hill, New York, 1972. J. J. Dongarra, C. B. Moler, J. R. Bunch & G. W. Stewart, LINPACK Users’ Guide, SIAM, Philadelphia, Pa., 1979.
- Bernard Friedman, Principles and techniques of applied mathematics, John Wiley & Sons, Inc., New York; Chapman & Hall, Ltd., London, 1956. MR 0079181
- Tosio Kato, Perturbation theory for linear operators, Die Grundlehren der mathematischen Wissenschaften, Band 132, Springer-Verlag New York, Inc., New York, 1966. MR 0203473
- J. H. Wilkinson, The algebraic eigenvalue problem, Clarendon Press, Oxford, 1965. MR 0184422
Additional Information
- © Copyright 1981 American Mathematical Society
- Journal: Math. Comp. 36 (1981), 1-19
- MSC: Primary 65L15
- DOI: https://doi.org/10.1090/S0025-5718-1981-0595038-4
- MathSciNet review: 595038