Yazar "Özdoğan, Nihal" seçeneğine göre listele

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    A Note on the Theory of Gamma and Beta Functions
    (Osman SAĞDIÇ, 2022) Özdoğan, Nihal
    Fizik ve mühendislik problemleri detaylı bir uygulamalı matematik bilgisini ve gamma ve beta fonksiyonları gibi özel fonksiyonların anlaşılmasını gerektirir. Özel fonksiyonlar konusu çok önemlidir ve uygulamalı bilimlerdeki yeni problemlerin varlığı ile sürekli genişlemektedir. Biz bu makalede, gamma ve beta fonksiyonlarının temel teorisini, birbirleriyle olan bağlantılarını ve mühendislik problemlerine uygulanabilirliklerini açıklıyoruz.
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    DYNAMICAL BEHAVIOURS OF A DISCRETIZED MODEL WITH MICHAELIS-MENTEN HARVESTING RATE
    (Gökhan ÇUVALCIOĞLU, 2022) Özdoğan, Nihal; Ongun, Mevlüde Yakıt
    In this paper, we introduced nonstandard finite difference scheme (NSFD) for solving the continuos model with Michaelis-Menten harvesting rate. We have seen that the proposed scheme preserve local stability and positivity. Stability analysis of each fixed point of the discrete time model has been proven. Also, numerical comparisons were made between the nonstandard finite difference method and the other methods.
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    Local Analysis of a Competitive Problem with Toxicants
    (Osman SAĞDIÇ, 2022) Özdoğan, Nihal
    This study aims to explain the dynamics of a competitive problem affected by toxicants. The effect of toxicants on ecological systems is an interesting topic for mathematical modelling. Discretization of the nonlinear problem is inevitable for right approximation of its solutions due to the difficulty of finding analytical solutions. In this work, a continuous time two species competitive problem was transformed into a discrete time problem. Because, it is very important to create a discrete model that will protect the properties of the original continuous model and the dynamics will be independent of step size. Also, in this study, the dynamic behaviour of a competitive system under the influence of toxicants were investigated. Lastly, the stability properties of each fixed point of the corresponding discrete problem have been examined using some theoretical results.
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    Nonstandard Finite Difference Scheme for a Computer Virus Model
    (Bursa Teknik Üniversitesi, 2020) Kocabıyık, Mehmet; Özdoğan, Nihal; Ongun, Mevlüde Yakıt
    This study introduces us to a new model developed for computer viruses. The model is presented to remove the protective restriction on the total number of computers connected to the Internet. This model is nonlinear differential equation system. Therefore, finding analytical solutions is very difficult. This means that we have to apply numerical methods in order to find the solution. The behavior of numerical solution has been investigated for the discretized system. By using Nonstandard Finite Difference Scheme (NSFD), it is aimed to preserve both the positivity of the solutions for positive initial points and the local asymptotic stability of the equilibrium point.