Browsing by Author "Biçer K.E."

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    A Novel Numerical Approach for Simulating the Nonlinear MHD Jeffery–Hamel Flow Problem
    (Springer, 2021) Adel W.; Biçer K.E.; Sezer M.
    The present study is related to the numerical simulation of the well-known Jeffery Hamel blood flow problem of nonlinear form. For the numerical solutions of the designed model, a Bernoulli collocation method is implemented. The method is based on converting the model into a system of a nonlinear algebraic equation which is then solved using a novel iterative technique. To check the perfection and exactness of the proposed schemes, two novel residual error correction methods are illustrated to ensure that the method is effective. The method does not require any extensive computational time while providing good results. Some numerical simulations are provided and a comparison is made with other existing methods from the literature. From these results, it can be seen that the Bernoulli collocation method is effective yet simple in providing accurate results for such a model. The method can be extended in the near future for solving similar other problems with applications in both science and engineering. © 2021, The Author(s), under exclusive licence to Springer Nature India Private Limited.
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    NUMERICAL METHOD BASED ON BOOLE POLYNOMIAL FOR SOLUTION OF GENERAL FUNCTIONAL INTEGRO-DIFFERENTIAL EQUATIONS WITH HYBRID DELAYS
    (Isik University, 2024) Biçer K.E.; Dag H.G.
    In this paper, the approximate solution of general functional integro differential equaions with hybrid delays is examined using of Boole polynomials and the collocation points. The solution is obtained as a truncated Boole series on a closed interval in the set of real numbers. By using this method, the approximate solutions of the problems are found. In addition, the error functions of the solutions are calculated by using the residual functions. Furthermore, the fundamental properties of the Boole polynomials and their generating functions are studied. Relationships between Boole polynomials and numbers, Stirling numbers and Euler polynomials and numbers are presented. TWMS Journal of Applied and Engineering Mathematics, Vol.14, No.3 © Işık University, Department of Mathematics, 2024; all rights reserved.