zbMATH — the first resource for mathematics

Geometry Search for the term Geometry in any field. Queries are case-independent.
Funct* Wildcard queries are specified by * (e.g. functions, functorial, etc.). Otherwise the search is exact.
"Topological group" Phrases (multi-words) should be set in "straight quotation marks".
au: Bourbaki & ti: Algebra Search for author and title. The and-operator & is default and can be omitted.
Chebyshev | Tschebyscheff The or-operator | allows to search for Chebyshev or Tschebyscheff.
"Quasi* map*" py: 1989 The resulting documents have publication year 1989.
so: Eur* J* Mat* Soc* cc: 14 Search for publications in a particular source with a Mathematics Subject Classification code (cc) in 14.
"Partial diff* eq*" ! elliptic The not-operator ! eliminates all results containing the word elliptic.
dt: b & au: Hilbert The document type is set to books; alternatively: j for journal articles, a for book articles.
py: 2000-2015 cc: (94A | 11T) Number ranges are accepted. Terms can be grouped within (parentheses).
la: chinese Find documents in a given language. ISO 639-1 language codes can also be used.

a & b logic and
a | b logic or
!ab logic not
abc* right wildcard
"ab c" phrase
(ab c) parentheses
any anywhere an internal document identifier
au author, editor ai internal author identifier
ti title la language
so source ab review, abstract
py publication year rv reviewer
cc MSC code ut uncontrolled term
dt document type (j: journal article; b: book; a: book article)
Correction of finite difference eigenvalues of periodic Sturm-Liouville problems. (English) Zbl 0676.65089
The known error in computation of higher eigenvalues in the Sturm- Liouville problem with constant potential function q is used to improve the accuracy of approximations for non-constant q which are obtained by the centered finite difference method with uniform mesh for problems with non-separated boundary conditions. The result is known for separated boundary conditions [cf. J. W. Paine, F. R. de Hoog and R. S. Anderssen, Computing 26, 123-139 (1981; Zbl 0436.65063)]. The author proves that the method is applicable to the boundary value problems (i), (ii) and (i), (iii) where (i)-y '' +q(x)y=λy, 0xπ, (ii)y(0)=y(π), y ' (0)=y ' (π), (iii)y(0)=-y(π), y ' (0)=-y ' (π) but is not applicable for (i), (iv) or (i), (v) when (iv)y(0)=-y(π), y ' (0)=y ' (π), (v)y(0)=y(π), y ' (0)=-y ' (π)· The results are confirmed by asymptotic analysis and numerical computations with q(x)=10cos(2x) and q(x)=x 2 (π-x)·
Reviewer: J.B.Butler jun.

65L15Eigenvalue problems for ODE (numerical methods)
34L99Ordinary differential operators