Makale Koleksiyonu
Bu koleksiyon için kalıcı URI
Güncel Gönderiler
Öğe Generalized differential transformation method for solving two-interval Weber equation subject to transmission conditions(KARAGANDA STATE UNIV, 2023) Yücel, Merve; Muhtarov, Fahreddin S.; Mukhtarov, Oktay Sh.The main goal of this study is to adapt the classical differential transformation method to solve new types of boundary value problems. The advantage of this method lies in its simplicity, since there is no need for discretization, perturbation or linearization of the differential equation being solved. It is an efficient technique for obtaining series solution for both linear and nonlinear differential equations and differs from the classical Taylor’s series method, which requires the calculation of the values of higher derivatives of given function. It is known that the differential transformation method is designed for solving single interval problems and it is not clear how to apply it to many-interval problems. In this paper we have adapted the classical differential transformation method for solving boundary value problems for two-interval differential equations. To substantiate the proposed new technique, a boundary value problem was solved for the Weber equation given on two non-intersecting segments with a common end, on which the left and right solutions were connected by two additional transmission conditions.Öğe Computation of Eigenfunctions of Nonlinear Boundary-Value -Transmission Problems by Developing Some Approximate Techniques(SOC PARANAENSE MATEMATICA, 2023) Yücel, Merve; Mukhtarov, Oktay Sh.; Aydemir, KadriyeIn this study, we investigate a boundary value problem for nonlinear Sturm-Liouville equations with additional transmission conditions at one interior singular point. Known numerical methods are intended for solving initial and boundary value problems without transmission conditions. By modifying the Adomian decomposition method and the differential transform method, we present a new numerical algorithm to com-pute the eigenvalues and eigenfunctions of the considered boundary-value-transmission problem. Some graphic illustrations of the approximate eigenfunctions are also presented.Öğe Abstract Korovkin theory in modular spaces in the sense of power series method(2018) Yurdakadim, TuğbaIn this paper, using the power series method we obtain an abstract Korovkin type approximation theorem for a sequence of positive linear operators dened on modular spaces.Öğe Treatment a New Approximation Method and Its Justification for Sturm-Liouville Problems(Wiley-Hindawi, 2020) Mukhtarov, Okan Sh.; Yücel, Merve; Aydemir, KadriyeIn this paper, we propose a new approximation method (we shall call this method as alpha-parameterized differential transform method), which differs from the traditional differential transform method in calculating the coefficients of Taylor polynomials. Numerical examples are presented to illustrate the efficiency and reliability of our own method. Namely, two Sturm-Liouville problems are solved by the present alpha-parameterized differential transform method, and the obtained results are compared with those obtained by the classical DTM and by the analytical method. The result reveals that alpha-parameterized differential transform method is a simple and effective numerical algorithm.Öğe A Study of the Eigenfunctions of the Singular Sturm-Liouville Problem Using the Analytical Method and the Decomposition Technique(Mdpi, 2020) Mukhtarov, Oktay Sh; Yücel, MerveAbstract: The history of boundary value problems for differential equations starts with the well-known studies of D. Bernoulli, J. D’Alambert, C. Sturm, J. Liouville, L. Euler, G. Birkhoff and V. Steklov. The greatest success in spectral theory of ordinary differential operators has been achieved for Sturm–Liouville problems. The Sturm–Liouville-type boundary value problem appears in solving the many important problems of natural science. For the classical Sturm–Liouville problem, it is guaranteed that all the eigenvalues are real and simple, and the corresponding eigenfunctions forms a basis in a suitable Hilbert space. This work is aimed at computing the eigenvalues and eigenfunctions of singular two-interval Sturm–Liouville problems. The problem studied here differs from the standard Sturm–Liouville problems in that it contains additional transmission conditions at the interior point of interaction, and the eigenparameter ? appears not only in the differential equation, but also in the boundary conditions. Such boundary value transmission problems (BVTPs) are much more complicated to solve than one-interval boundary value problems ones. The major difficulty lies in the existence of eigenvalues and the corresponding eigenfunctions. It is not clear how to apply the known analytical and approximate techniques to such BVTPs. Based on the Adomian decomposition method (ADM), we present a new analytical and numerical algorithm for computing the eigenvalues and corresponding eigenfunctions. Some graphical illustrations of the eigenvalues and eigenfunctions are also presented. The obtained results demonstrate that the ADM can be adapted to find the eigenvalues and eigenfunctions not only of the classical one-interval boundary value problems (BVPs) but also of a singular two-interval BVTPs.Öğe A New Treatment of the Decomposition Method for Nonclassical Boundary Value Problems(Amer Scientific Publishers, 2018) Yücel, Merve; Mukhtarov, Oktay Sh.In this work, we will adapt the Adomian Decomposition Method to nonclassical boundary value problems the main feature of which is the nature of the equations and the boundary conditions imposed. Namely, the boundary conditions contains not only end points of the considered interval, but also a interior point of singularity at which given additional so-called transmission conditions, so our problem is the nonclassical once. Based on decomposition method and our own approaches a new analytical treatment is introduced for such type transmission problems. By comparision with the exact solutions we show that the Adomian decomposition method (ADM) is an efficient method for solving nonclassical Sturm-Liouville type problems under supplementary transmission conditions.Öğe Open book decompositions of links of quotient surface singularities and support genus problem(American Institute of Mathematical Sciences, 2019) Dalyan, ElifAbstract: In this paper we write explicitly the open book decompositions of links of quotient surface singularities supporting the corresponding unique Milnor fillable contact structure. The page-genus of these Milnor open books are minimal among all Milnor open books supporting the same contact structure. We also investigate whether the Milnor genus is equal to the support genus for links of quotient surface singularities. We show that for many types of the quotient surface singularities the Milnor genus is equal to the support genus. In the remaining cases we are able to find a small upper bound for the support genus.Öğe Maximal sectorial differential operators for first order(2015) Ismailov, Zameddin I.; Öztürk Mert, RukiyeIn this study, the maximal sectorial linear relations are described. Then, the discreteness of the spectrum of the linear maximal sectorial operators and asymptotical behavior of the eigenvalues of such operators in terms of the eigenvalues of its real part are investigated. Moreover, one result for the differential operators for first order in the Hilbert space of vector functions in finite interval is obtained.Öğe On the spectrums of some class of selfadjoint singular differential operators(Ankara University, 2016) Ismailov, Zameddin I.; Yılmaz, Bülent; Öztürk Mert, RukiyeAbstract. In this work, based on the Everitt-Zettl and Calkin-Gorbachuk methods in terms of boundary values all selfadjoint extensions of the minimal operator generated by some linear singular multipoint symmetric differentialoperator expression for first order in the direct sum of Hilbert spaces of vectorfunctions on the right semi-axis are described. Later structure of the spectrum of these extensions is investigated.Öğe Some Korovkin type results via power series method in modular spaces(Ankara University, 2016) Yurdakadim, TuğbaAbstract. In this paper, we obtain a Korovkin type approximation result for a sequence of positive linear operators deÖned on modular spaces with the use of power series method . We also provide an example which satisfies our theorem.Öğe A trace formula for the sturm-liouville type equation with retarded argument(Ankara Üniversitesi, 2017) Hıra, FatmaIn this paper, we deal with a discontinuous Sturm-Liouville problem with retarded argument and eigenparameter-dependent boundary conditions. We obtain the asymptotic formulas for the eigenvalues and the regularized trace formula for the problem.Öğe The Arzelà-Ascoli theorem by means of ideal convergence(De Gruyter, 2018) Taş, Emre; Yurdakadim, TuğbaIn this paper, using the concept of ideal convergence, which extends the idea of ordinary convergence and statistical convergence, we are concerned with the I-uniform convergence and the I-pointwise convergence of sequences of functions defined on a set of real numbers D. We present the Arzelà-Ascoli theorem by means of ideal convergence and also the relationship between I-equicontinuity and I-continuity for a family of functions. © 2018 Walter de Gruyter GmbH, Berlin/Boston.Öğe Normal extensions of a singular differential operator on the right semi-axis(Eurasian Mathematical Journal, 2014) Ismailov, Zameddin I.; Öztürk Mert, RukiyeIn this work, based on the method of Everitt-Zettl and using the Calkin-Gorbachuk method, all normal extensions of the minimal operator generated by a linear singular formally normal differential-operator expression of the first order in Hilbert spaces of vector-functions on the right semi-axis in terms of boundary values are described. Furthermore, the structure of the spectrum of these extensions is investigated. © The Eurasian National University.Öğe Korovkin type approximation theorems in weighted spaces via power series method(Element D.O.O., 2018) Taş, Emre; Yurdakadim, Tuğba; Girgin Atlıhan, ÖzlemIn this paper we consider power series method which is also member of the class of all continuous summability methods. We study a Korovkin type approximation theorem for a sequence of positive linear operators acting from a weighted space C?1 into a weighted space B?2 with the use of the power series method which includes both Abel and Borel methods. We also consider the rates of convergence of these operators. © 2018, Element D.O.O.. All rights reserved.Öğe The regularized trace of Sturm–Liouville problem with discontinuities at two points(Taylor and Francis Ltd., 2017) Hıra, FatmaIn this paper, we obtain a regularized trace formula for a Sturm–Liouville problem which has two points of discontinuity and also contains an eigenparameter in a boundary condition. © 2016 Informa UK Limited, trading as Taylor & Francis Group.Öğe Sturm-Liouville problem with moving discontinuity points(Springer International Publishing, 2015) Hıra, Fatma; Altınışık, NihatIn this paper, we present a new discontinuous Sturm-Liouville problem with symmetrically located discontinuities which are defined depending on a parameter in the neighborhood of an interior point in the interval. Also the problem contains an eigenparameter in a boundary condition. We investigate some spectral properties of the eigenvalues, obtain asymptotic formulae for the eigenvalues and the corresponding eigenfunctions and construct Green’s function for the problem. We give an illustrative example with tables and figures at the end of the paper. © 2015, Hıra and Altınışık.Öğe Some inequalities between functionals related to generalized limits(Editura Academiei Romane, 2017) Yurdakadim, Tuğba; Orhan, CihanRecall that A-statistical core theorem determines a class of regular matrices for which lim sup(T x) ? stA ? lim sup x for all x ? m. The main object of this paper is to study an inequality between functionals which is sharper than that of the A-statistical core theorem. We also study the relationship between these functionals and some generalized limits which are called SA-limits and A-Banach limits.Öğe Approximation by positive linear operators in modular spaces by power series method(Birkhauser Verlag AG, 2017) Taş, Emre; Yurdakadim, TuğbaIn the present paper, we study the problem of approximation to a function by means of positive linear operators in modular spaces in the sense of power series method. Indeed, in order to get stronger results than the classical cases, we use the power series method which also includes both Abel and Borel methods. An application that satisfies our theorem is also provided. © 2017, Springer International Publishing.Öğe A note on the generalized Matsumoto relation(TUBİTAK, 2017) Dalyan, Elif; Medetoğulları, Elif; Pamuk, MehmetcikWe give an elementary proof of a relation, first discovered in its full generality by Korkmaz, in the mapping class group of a closed orientable surface. Our proof uses only the well-known relations between Dehn twists. © TÜBİTAK.Öğe Some results concerning the summability of spliced sequences(TUBİTAK, 2016) Yurdakadim, Tuğba; Ünver, MehmetA spliced sequence is formed by combining all of the terms of two or more convergent sequences, in their original order, into a new spliced sequence. In this paper replacing convergent sequences by bounded sequences, we study the summability of spliced sequences and give some inequalities that provide us with approximation of the core of transformation of these sequences by a summability matrix. We also present some further results via the Lebesgue integral. © Tübi?tak.
