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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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    Öğe
    Treatment a New Approximation Method and Its Justification for Sturm-Liouville Problems
    (Wiley-Hindawi, 2020) 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.