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Robni problemi za nelinearne diferencialne enačbe drugega redaHladnik, MilanSestavek obravnava na elementaren način teorijo eksistence in enoličnosti za robni problem, pripadajoč navadni diferencialni enačbi drugege reda ▫$y''+ f(t,y,y') = 0$▫. Pri tem se skoraj izključno ... omejuje na robne pogoje oblike ▫$y(a) = A, \; y(b) = B$▫ (prve vrste) in ▫$y(a) = A, \; y'(b) = m$▫ ali ▫$y'(a) = m, \; y(b) = B$▫ (druge vrste). Numeričnih metod za reševanje ne navaja. Medtem, ko drugi razdelek uporablja pri eksistenčnem dokazu princip o skrčenih slikah, pa ostala poglavja razvijajo eksistenčno teorijo s pomočjo ustreznih začetnih problemov. Glavni rezultat je priporočen kriterij, ki nam napove, kako velik je lahko še interval, da na njem eksistira ena sama rešitev robnega problema.Type of material - bookPublication and manufacture - Ljubljana : FNT, Odsek za matematiko, 1972Language - slovenianCOBISS.SI-ID - 9512537
Author
Hladnik, Milan
Topics
matematika |
analiza |
navadne diferencialne enačbe |
robni problemi |
Picardova iteracija |
izreki o enoličnosti |
primerjalni izreki |
eksistenčni izreki |
mathematics |
analysis |
ordinary differential equations |
boundary value problems |
Picard's iteration |
existence theorems |
uniqueness of solutions
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