Iterated defect correction methods for semi-explicit differential-algebraic equations

Somalı(Uzuner), Şennur


Asymptotic integration of impulsive differential equations
Doğru Akgöl, Sibel; Ağacık, Zafer; Özbekler, Abdullah; Department of Mathematics (2017)
The main objective of this thesis is to investigate asymptotic properties of the solutions of differential equations under impulse effect, and in this way to fulfill the gap in the literature about asymptotic integration of impulsive differential equations. In this process our main instruments are fixed point theorems; lemmas on compactness; principal and nonprincipal solutions of impulsive differential equations and Cauchy function for impulsive differential equations. The thesis consists of five chapters....
Stochastic delay differential equations
Aladağlı, E. Ezgi; Yolcu Okur, Yeliz; Vardar Acar, Ceren; Department of Financial Mathematics (2017)
In many areas of science like physics, ecology, biology, economics, engineering, financial mathematics etc. phenomenas do not show their effect immediately at the moment of their occurrence. Generally, they influence the future states. In order to understand the structure and quantitative behavior of such systems, stochastic delay differential equations (SDDEs) are constructed while inserting the information that are obtained from the past phenomena into the stochastic differential equations (SDEs). SDDEs b...
Oscillation of second order matrix equations on time scales
Selçuk, Aysun; Ağacık, Zafer; Department of Mathematics (2004)
The theory of time scales is introduced by Stefan Hilger in his PhD thesis in 1998 in order to unify continuous and discrete analysis. In our thesis, by making use of the time scale calculus we study the oscillation of nonlinear matrix differential equations of second order. the first chapter is introductory in nature and contains some basic definitions and tools of the time scales calculus, while certain well-known results have been presented with regard to oscillation of the solutions of second order matr...
Oscillation of second order dynamic equations on time scales
Kütahyalıoğlu, Ayşen; Ağacık, Zafer; Department of Mathematics (2004)
During the last decade, the use of time scales as a means of unifying and extending results about various types of dynamic equations has proven to be both prolific and fruitful. Many classical results from the theories of differential and difference equations have time scale analogues. In this thesis we derive new oscillation criteria for second order dynamic equations on time scales.
Differential equations with discontinuities and population dynamics
Aruğaslan Çinçin, Duygu; Akhmet, Marat; Department of Mathematics (2009)
In this thesis, both theoretical and application oriented results are obtained for differential equations with discontinuities of different types: impulsive differential equations, differential equations with piecewise constant argument of generalized type and differential equations with discontinuous right-hand sides. Several qualitative problems such as stability, Hopf bifurcation, center manifold reduction, permanence and persistence are addressed for these equations and also for Lotka-Volterra predator-...
Citation Formats
Ş. Somalı(Uzuner), “Iterated defect correction methods for semi-explicit differential-algebraic equations,” Ph.D. - Doctoral Program, Middle East Technical University, 1990.