Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

Online ISSN 1552-4485; Print ISSN 0033-569X



Asymptotic expansions of eigenvalues and eigenfunctions of random boundary value problems

Author: William B. Day
Journal: Quart. Appl. Math. 38 (1980), 169-177
MSC: Primary 35P10
DOI: https://doi.org/10.1090/qam/580877
MathSciNet review: 580877
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: An asymptotic procedure is developed for calculating the eigenvalues and eigenfunctions of linear boundary-value problems which may contain random coefficients in the operator. The corresponding asymptotic series for the solution of a second-order initial-value problem is shown to be convergent.

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

  • [1] A. T. Bharucha-Reid, Random integral equations, Academic Press, New York, 1972 MR 0443086
  • [2] W. E. Boyce, A ``dishonest'' approach to certain stochastic eigenvalue problems, SIAM J. Appl. Math. 15, 143-152 (1967) MR 0212307
  • [3] W. E. Boyce, Random eigenvalue problems, in Probabilistic methods in applied mathematics, vol. 1 (A. T. Bharucha-Reid, ed.), Academic Press, New York, 1968, 1-73 MR 0263171
  • [4] W. E. Boyce, Random vibrations of elastic strings and bars, in Proc. U.S. Nat. Congr. Appl. Mech. (4th), Berkeley, 1962, 77-85, Amer. Soc. Mech. Eng., New York, 1962 MR 0152193
  • [5] W. E. Boyce, Stochastic nonhomogeneous Sturm-Liouville problems, J. Franklin Inst. 282, 206-215 (1966) MR 0204797
  • [6] W. E. Boyce and B. E. Goodwin, Random transverse vibrations of elastic beams, SIAM J. 12, 613-629 (1964) MR 0175396
  • [7] W. B. Day, More bounds for eigenvalues. J. Math. Anal. Appl. 46, 523-532 (1974) MR 0356523
  • [8] W. B. Day, More eigenvalue estimates, Appl. Math. Comput. 1, 325-331 (1975) MR 0413519
  • [9] B. E. Goodwin and W. E. Boyce, Vibrations of random elastic strings: method of integral equations, Quart. Appl. Math. 22, 261-266 (1964)
  • [10] C. W. Haines, Hierarchy methods for random vibrations of elastic strings and beams, in Proc. U.S. Nat. Cong. Appl. Mech. (5th), Minneapolis, 1966
  • [11] W. Leighton, Upper and lower bounds for eigenvalues, J. Math. Anal. Appl. 35, 381-388 (1971) MR 0281334
  • [12] W. Purkert and J. vom Scheidt, Zur approximativen Lösung des Mittelungsproblems für die eigenwerte stochastischer Differentialoperatoren, ZAMM 57, 515-525 (1977) MR 480129
  • [13] T. T. Soong, Random differential equations, Academic Press, New York, 1973 MR 0451405
  • [14] T. T. Soong and J. L. Bogdanoff, On the natural frequencies of a disordered linear chain on N degrees of freedom, Int. J. Mech. Sci. 5, 237-265 (1963)
  • [15] T. van Karman and M. A. Biot, Mathematical methods in engineering, McGraw-Hill, New York, 1940

Similar Articles

Retrieve articles in Quarterly of Applied Mathematics with MSC: 35P10

Retrieve articles in all journals with MSC: 35P10

Additional Information

DOI: https://doi.org/10.1090/qam/580877
Article copyright: © Copyright 1980 American Mathematical Society

American Mathematical Society