Yazar "Mukhtarov, Oktay Sh." seçeneğine göre listele

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    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.
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    Computation of Eigenfunctions of Nonlinear Boundary-Value -Transmission Problems by Developing Some Approximate Techniques
    (SOC PARANAENSE MATEMATICA, 2023) 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.
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    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.