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    REPRODUCING KERNEL FUNCTIONS AND HOMOGENIZING TRANSFORMS
    (Vinca Inst Nuclear Sci, 2021) Yildirim, Elif Nuray; Akgul, Ali; Inc, Mustafa
    A lot of problems of the physical world can be modeled by non-linear ODE with their initial and boundary conditions. Especially higher order differential equations play a vital role in this process. The method for solution and its effectiveness are as important as the modelling. In this paper, on the basis of reproducing kernel theory, the reproducing kernel functions have been obtained for solving some non-linear higher order differential equations. Additionally, for each problem the homogenizing transforms have been obtained.
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    Öğe
    Reproducing kernel method for the solutions of non-linear partial differential equations
    (Taylor and Francis Ltd., 2021) Yildirim, Elif Nuray; Akgül, Ali; Inc, Mustafa
    In modeling of a lots of complex physical problems and engineering process, the non-linear partial differential equations have a very important role. Development of dependable and effective methods to solve such types equations are constructed. In the suggested technique, reproducing kernel method is examined to approximate the solutions together with reproducing kernel functions. In order to demonstrate accuracy, the performance and reliability of the proposed method, the results of the experiments and the available results are compared. There is high stability for a higher degree of accuracy between the solutions. © 2021 The Author(s). Published by Informa UK Limited, trading as Taylor & Francis Group on behalf of the University of Bahrain.