The positivity of the second order difference operator with periodic conditions in Hölder spaces and its applications.
In: AIP Conference Proceedings; 2014, Vol. 1611, p336-343, 8p; Jg. 1611 (2014-08-20) S. 336-343
Konferenz
Zugriff:
In this study, the second order of approximation of the difference operator Af approximates the second order differential operator Ax defined by the formula A x u = -u xx (x) + δu(x),δ > 0 with domain D(A x ) = {u(x) : u(x),u!(x),u"(x) e ∊ (R¹), u(x) = u(x + 2π),x ∊ R¹, ...u(x)dx = 0} is considered. The Green's function of the difference operator A h x is constructed. The estimates for the Green's function are obtained. The positivity of operator A h x in the Banach space C (R 1h ) of periodic mesh functions defined on R 1h is established. Here, R 1h = {x k = kh,k = 0, ∓1, ∓2,...}. It is proved that for any α ∊ (0, 1/2), the norms in spaces E α = E α (C(R 1h ),A h x ) and C 2α (R 1h ) are equivalent uniformly with respect to h. The positivity of the operator A h x in Hölder spaces of C 2α (R 1h ), α ∊ (0, 1/2 ) is proved. We discuss its applications to theory of difference schemes forthe approximate solution of local and nonlocal boundary value problems for elliptic differential equations. [ABSTRACT FROM AUTHOR]
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Titel: |
The positivity of the second order difference operator with periodic conditions in Hölder spaces and its applications.
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Autor/in / Beteiligte Person: | Ashyralyev, Allaberen ; Tetikoglu, Fatih Sabahattin |
Quelle: | AIP Conference Proceedings; 2014, Vol. 1611, p336-343, 8p; Jg. 1611 (2014-08-20) S. 336-343 |
Veröffentlichung: | 2014 |
Medientyp: | Konferenz |
ISSN: | 0094-243X (print) |
DOI: | 10.1063/1.4893857 |
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