Numerical Verifications for Eigenvalues of Second-Order Elliptic Operators

Japan Journal of Industrial and Applied Mathematics

Volumn 16, Issue 3, 1999, Pages 307-320

  Nakao, M T ^a   Yamamoto, N ^a   Nagatou, K ^a  

^a KYUSHU UNIVERSITY   (Japan)

Author keywords

Eigenvalue problem; Elliptic operators; Error estimates; Finite element solution

Indexed keywords

EID: 0000218518     PISSN: 09167005     EISSN: None     Source Type: Journal    
DOI: 10.1007/BF03167360     Document Type: Article

References (17)

1. H. Behnke and F. Goerisch, Inclusions for eigenvalues of selfadjoint problems. Topics in Validated Computations-Studies in Computational Mathematics (ed. J. Herzberger), Elsevier, Amsterdam, 1994.
2. P. Grisvard, Elliptic problems in nonsmooth domains. Pitman Monographs and Survays in Pure and Applied Mathematics, 24, London, 1985.
3. O. Knüppel, PROFIL/BIAS - A fast interval library. Computing, 53 (1994), 277-288.
4. M. Křížek and P. Neittaanmäki, Finite Element Approximation of Variational Problems and Applications. Longman Scientific and Technical, Harlow, 1990.
5. M.T. Nakao, A numerical approach to the proof of existence of solutions for elliptic problems. Japan J. Appl. Math., 5 (1988), 313-332.
6. M.T. Nakao, A numerical approach to the proof of existence of solutions for elliptic problems II. Japan J. Appl. Math., 7 (1990), 477-488.
7. M.T. Nakao, A numerical verification method for the existence of weak solutions for non-linear boundary value problems. J. Math. Anal. Appl., 164 (1992), 489-507.
8. -1 type residual iteration. Computing, Suppl., 9 (1993), 161-173.
9. ∞ residual method. J. Math. Anal. Appl., 217 (1998), 246-262.
10. M. Plum, Eigenvalue inclusions for second-order ordinary differential operators by a numerical homotopy method. J.Appl.Math.Phys.(ZAMP), 41 (1990), 205-226.
11. M. Plum, Bounds for eigenvalues of second-order elliptic differential operators. J. Appl. Math. Phys. (ZAMP), 42 (1991), 848-863.
12. 2-estimates and pointwise bounds for solutions of second-order elliptic boundary value problems. J. Math. Anal. Appl., 165 (1992), 36-61.
13. M. Plum, Existence and enclosure results for continua of solutions of parameter-dependent nonlinear boundary value problems. J. Comput. Appl. Math., 60 (1995), 187-200.
14. S.M. Rump, Solving algebraic problems with high accuracy. A New Approach to Scientific Computation (eds. U. Kulisch and W.L. Miranker), Academic Press, New York. 1983.
15. Y. Watanabe and M.T. Nakao, Numerical verifications of solutions for nonlinear elliptic equations. Japan J. Indust. Appl. Math., 10 (1993), 165-178.
16. N. Yamamoto and M.T. Nakao, Numerical verifications for solutions to elliptic equations using residual iterations with a high order finite element. J. Comput. Appl. Math., 60 (1995),271-279.
17. E. Zeidler, Nonlinear Functional Analysis and its Applications I. Springer, New York, 1986.