Diferencialne enačbe z zamikom

delo diplomskega seminarja

David Rozman (Author), Uroš Kuzman (Mentor)

Abstract

Diferencialne enačbe z zamikom povezujejo odvod funkcije z njenimi vrednosti v preteklem času. Začetni pogoj je podan kot funkcija na ustreznem intervalu. Pogoji za obstoj in enoličnost rešitve takega začetnega problema so podobni kot pri navadnih diferencialnih enačbah, vendar pa rešitve pogosto niso zvezne in odvedlijve. V nalogi je predstavljenih nekaj standardnih metod za reševanje izbranih tipov enačb, analizirana pa sta tudi zamaknjena modela eksponentne in logistične rasti.

Keywords

matematika;diferencialne enačbe;zamik;eksistenčni izrek;Laplaceova transformacija;logistična funkcija;

Data

Language:	Slovenian
Year of publishing:	2022
Typology:	2.11 - Undergraduate Thesis
Organization:	UL FMF - Faculty of Mathematics and Physics
Publisher:	[D. Rozman]
UDC:	517.9
COBISS:	119326467
Views:	778
Downloads:	56
Average score:	0 (0 votes)
Metadata:

Other data

Secondary language:	English
Secondary title:	Delay differential equations
Secondary abstract:	Delay differential equations connect the derivative of a function with its value in a previous state. The initial condition is given as a function over a certain interval. The conditions for existence and uniqueness of a solution are similar to those for ordinary differential equations, yet the solution is often neither differentiable nor continuous. In this thesis I present some of the standard methods for solving certain types of delay differential equations and analyse delayed exponential and logistic growth models.
Secondary keywords:	mathematics;differential equations;delay;existence theorem;Laplace transform;logistic function;
Type (COBISS):	Final seminar paper
Study programme:	0
Thesis comment:	Univ. v Ljubljani, Fak. za matematiko in fiziko, Oddelek za matematiko, Finančna matematika - 1. stopnja
Pages:	25 str.
ID:	16279614