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  • 1
    Electronic Resource
    Electronic Resource
    Correction of finite element eigenvalues for problems with natural or periodic boundary conditions (1988)
    Springer
    BIT 28 (1988), S. 254-269 
    Details
    ISSN: 1572-9125
    Keywords: 65L15 ; 65L60 ; asymptotic correction ; Sturm-Liouville eigenvalues ; finite element method ; natural boundary conditions ; periodic boundary conditions
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract Recent results of Andrew and Paine for a regular Sturm-Liouville problem with essential boundary conditions are extended to problems with natural or periodic boundary conditions. These results show that a simple asymptotic correction technique of Paine, de Hoog and Anderssen reduces the error in the estimate of thekth eigenvalue obtained by the finite element method, with linear hat functions and mesh lengthh, fromO(k 4 h 2) toO(kh 2). Numerical results show the correction to be useful even for low values ofk.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01934090
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    Paper (German National Licenses)
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  • 2
    Electronic Resource
    Electronic Resource
    Correction of Numerov's eigenvalue estimates (1985)
    Springer
    Numerische Mathematik 47 (1985), S. 289-300 
    Details
    ISSN: 0945-3245
    Keywords: AMS(MOS): 65L15 ; CR: G1.7
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary The error in the estimate of thekth eigenvalue of a regular Sturm-Liouville problem obtained by Numerov's method with mesh lengthh isO(k 6 h 4). We show that a simple correction technique of Paine, de Hoog and Anderssen reduces the error to one ofO(k 3 h 4). Numerical examples demonstrate the usefulness of this correction even for low values ofk.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01389712
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    Paper (German National Licenses)
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  • 3
    Electronic Resource
    Electronic Resource
    Correction of finite element estimates for Sturm-Liouville eigenvalues (1986)
    Springer
    Numerische Mathematik 50 (1986), S. 205-215 
    Details
    ISSN: 0945-3245
    Keywords: AMS(MOS): 65L15 ; CR: G1.7
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary It is shown that a simple asymptotic correction technique of Paine, de Hoog and Anderssen reduces the error in the estimate of thekth eigenvalue of a regular Sturm-Liouville problem obtained by the finite element method, with linear hat functions and mesh lengthh, fromO(k 4 h 2) toO(k h 2). The result still holds when the matrix elements are evaluated by Simpson's rule, but if the trapezoidal rule is used the error isO(k 2 h 2). Numerical results demonstrate the usefulness of the correction even for low values ofk.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01390430
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    Paper (German National Licenses)
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  • 4
    Electronic Resource
    Electronic Resource
    Iterative computation of second-order derivatives of eigenvalues and eigenvectors (1994)
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 10 (1994), S. 1-9 
    Details
    ISSN: 1069-8299
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: An iterative method is introduced for computing second-order partial derivatives (sensitivities) of eigenvalues and eigenvectors of matrices which depend on a number of real design parameters. Numerical tests confirm the viability of the method and support our theoretical analysis. Alternative methods are reviewed briefly and compared with the one proposed here.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/cnm.1640100102
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    Paper (German National Licenses)
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