Yazar "Ozdogan, Nihal" seçeneğine göre listele

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    Applications of Mohand Transform
    (2024) Ozdogan, Nihal
    Investigating solutions of differential equations has been an important issue for scientists. Researchers around the world have talked about different methods to solve differential equations. The type and order of the differential equation enable us to decide the method that we can choose to find the solution of the equation. One of these methods is the integral transform, which is the conversion of a real or complex valued function into another function by some algebraic operations. Integral transforms are used to solve many problems in mathematics and engineering, such as differential equations and integral equations. Therefore, new types of integral transforms have been defined, and existing integral transforms have been improved. One of the solution methods of many physical problems as well as initial and boundary value problems are integral transforms. Integral transforms were introduced in the first half of the 19th century. The first historically known integral transforms are Laplace and Fourier transforms. Over the time, other transforms that are used in many fields have emerged. The aim of this article is to describe the Mohand transform and to make applications of linear ordinary differential equations with constant coefficients without any major mathematical calculations This integral transform method is an alternative method to existing transforms such as Laplace transform and Kushare transform. When recent studies in the literature are examined, it can be said that Mohand transform is preferred because it is easy to apply.
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    Comparison of the results obtained by Iman transform with Laplace transform
    (2024) Ozdogan, Nihal
    Many processes in the real world are characterised by principles which are defined in the form of expressions involving rates of change. Mathematically, rates are derivatives and expressions are equations so we have differential equations. Differential equations play an important role for modelling many problems in different scientific fields. Sometimes, the calculations to solve these equations can be very complex and ultimately frustrating. For this reason, many integral transform methods were proposed by researchers. However, integral transform methods can give consistent solutions to many complex problems and have many application areas such as physics, mechanics, engineering, astronomy. In this work, two integral transforms, Iman transform and the well-known Laplace transform were studied comparatively to facilitate the solution of linear ordinary differential equations with constant coefficients. Applications of these two transforms show that these integral transform methods are closely related to each other.
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    Nonstandard Finite Difference Theta Approaches to the Predator-Prey System
    (Wiley, 2026) Ozdogan, Nihal; Arslan, Bahar
    In this paper, we propose nonstandard finite difference theta schemes for a well-known Lotka-Volterra model without the Allee effect and investigate the dynamical behavior of the discretized system. We prove that the scheme is dynamically consistent with the continuous model, preserving key properties such as the positivity of solutions and the stability of equilibrium points. Numerical experiments are conducted to validate the theoretical results and demonstrate the superiority of the proposed schemes over standard methods in maintaining these critical properties.