Makale Koleksiyonu
https://hdl.handle.net/11491/2157
Article Colleciton2024-03-29T06:10:28ZGeneralized differential transformation method for solving two-interval Weber equation subject to transmission conditions
https://hdl.handle.net/11491/8784
Generalized differential transformation method for solving two-interval Weber equation subject to transmission conditions
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.
2023-01-01T00:00:00ZComputation of Eigenfunctions of Nonlinear Boundary-Value -Transmission Problems by Developing Some Approximate Techniques
https://hdl.handle.net/11491/8748
Computation of Eigenfunctions of Nonlinear Boundary-Value -Transmission Problems by Developing Some Approximate Techniques
Yücel, Merve; Mukhtarov, Oktay Sh.; Aydemir, Kadriye
In 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.
2023-01-01T00:00:00ZAbstract Korovkin theory in modular spaces in the sense of power series method
https://hdl.handle.net/11491/7577
Abstract Korovkin theory in modular spaces in the sense of power series method
Yurdakadim, Tuğba
In 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.
2018-01-01T00:00:00ZTreatment a New Approximation Method and Its Justification for Sturm-Liouville Problems
https://hdl.handle.net/11491/7189
Treatment a New Approximation Method and Its Justification for Sturm-Liouville Problems
Mukhtarov, Okan Sh.; Yücel, Merve; Aydemir, Kadriye
In 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.
2020-01-01T00:00:00Z