Different convergences in approximation of evolution equations
| dc.contributor.author | Piskarev, S. | |
| dc.date.accessioned | 2024-07-12T20:50:08Z | |
| dc.date.available | 2024-07-12T20:50:08Z | |
| dc.date.issued | 2009 | en_US |
| dc.department | Fakülteler, İnsan ve Toplum Bilimleri Fakültesi, Matematik Bölümü | en_US |
| dc.description.abstract | Consider the semilinear equation in Banach space E ? u 0 (t) = Au(t) + f(u(t)), t ? 0, u(0) = u 0 ? E ?, (0.1) where f(·) : E ? ? E ? E, 0 ? ? < 1, is assumed to be continuous, bounded and continuously Fr´echet differentiable function. The problem (0.1) in the neighborhood of the hyperbolic equilibrium can be written in the form, where Au? = A+f 0 (u ? ), Fu? (v(t)) = f(v(t)+u ? )?f(u ? )?f 0 (u ? )v(t). We consider approximation of (0.2) by the following scheme, with initial data Vn(0) = v 0 n. The solution of such problem is given by formula Vn(t + ?n) = (In ? ?nAu? n,n) ?1Vn(t) + ?n(In ? ?nAu? n,n) ?1Fu? n,n(Vn(t)) = = (In ? ?nAu? n,n) ?kVn(0) + ?n? k j=0(In ? ?nAu? n,n) ?(k?j+1)Fu? n,n(Vn(j?n)), t = k?n, where Vn(0) = v 0 n. We consider different kind of consistency of generators under which one can get convergence of solutions in the vicinity of hyperbolic stationary point. | en_US |
| dc.identifier.citation | Piskarev, S. (2009). Different convergences in approximation of evolution equations. Maltepe Üniversitesi. s. 352. | en_US |
| dc.identifier.endpage | 353 | en_US |
| dc.identifier.isbn | 9.78605E+12 | |
| dc.identifier.startpage | 352 | en_US |
| dc.identifier.uri | https://hdl.handle.net/20.500.12415/2283 | |
| dc.institutionauthor | Piskarev, S. | |
| dc.language.iso | en | en_US |
| dc.publisher | Maltepe Üniversitesi | en_US |
| dc.relation.ispartof | International Conference of Mathematical Sciences | en_US |
| dc.relation.publicationcategory | Uluslararası Konferans Öğesi - Başka Kurum Yazarı | en_US |
| dc.rights | CC0 1.0 Universal | * |
| dc.rights | info:eu-repo/semantics/openAccess | en_US |
| dc.rights.uri | http://creativecommons.org/publicdomain/zero/1.0/ | * |
| dc.snmz | KY07610 | |
| dc.title | Different convergences in approximation of evolution equations | en_US |
| dc.type | Conference Object | |
| dspace.entity.type | Publication |
