| Title:
|
On a method of two-sided eigenvalue estimates for elliptic equations of the form $Au-\lambda Bu=0$ (English) |
| Author:
|
Rektorys, Karel |
| Author:
|
Vospěl, Zdeněk |
| Language:
|
English |
| Journal:
|
Aplikace matematiky |
| ISSN:
|
0373-6725 |
| Volume:
|
26 |
| Issue:
|
3 |
| Year:
|
1981 |
| Pages:
|
211-240 |
| Summary lang:
|
English |
| Summary lang:
|
Czech |
| . |
| Category:
|
math |
| . |
| Summary:
|
The Collatz method of twosided eigenvalue estimates was extended by K. Rektorys in his monography Variational Methods to the case of differential equations of the form $Au - \lambda Bu=0$ with elliptic operators. This method requires to solve, successively, certain boundary value problems. In the case of partial differential equations, these problems are to be solved approximately, as a rule, and this is the source of further errors. In the work, it is shown how to estimate these additional errors, or how to avoid them by a proper modification of the method. At the same time, some results of their own interest are derived. (English) |
| Keyword:
|
Collatz method |
| Keyword:
|
twosided eigenvalue estimates |
| Keyword:
|
elliptic operators |
| MSC:
|
35P15 |
| MSC:
|
49G05 |
| MSC:
|
65N15 |
| MSC:
|
65N25 |
| MSC:
|
65N30 |
| idZBL:
|
Zbl 0474.65080 |
| idMR:
|
MR0615608 |
| DOI:
|
10.21136/AM.1981.103913 |
| . |
| Date available:
|
2008-05-20T18:17:02Z |
| Last updated:
|
2020-07-28 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/103913 |
| . |
| Reference:
|
[1] K. Rektorys: Variational Methods in Mathematics, Science and Engineering.Reidel Publ. Co., Dortrecht (Holland)-Boston (USA) 1977. (In Czech: Praha, SNTL, 1974.) MR 0487653 |
| Reference:
|
[2] L. Collatz: Eigenwertaufgaben mit technischen Anwendungen.2nd Ed. Leipzig, Geert and Portig 1963. MR 0152101 |
| Reference:
|
[3] L. Collatz: Functional Analysis and Numerical Mathematics.New York, Academic Press 1966. MR 0205126 |
| Reference:
|
[4] Z. Vospěl: Some Eigenvalue Estimates for Partial Differential Equations of the Form $Au - \lambda Bu = 0$.Dissertation, Technical University Prague, 1978. (In Czech.) |
| Reference:
|
[5] P. G. Ciarlet M. H. Schulz R. S. Varga: Numerical Methods of High-Order Accuracy for Nonlinear Boundary Value Problems. Part III, Eigenvalue Problems.Num. Math 12 (1968), 120-133. MR 0233517, 10.1007/BF02173406 |
| Reference:
|
[6] A. K. Azis: The Mathematical Foundations of the Finite Element Method with Applications to Partial Differential Equations.Part I by I. Babuška and A. K. Azis, 3-359. Academic Press, New York-London, 1972. MR 0347104 |
| . |
