Browsing by Publisher "Springer Medizin"

Now showing 1 - 5 of 5
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    Freeness conditions for quasi 3-crossed modules and complexes of using simplicial algebras with C W−bases
    (Springer Medizin, 2013) Mutlu A.; Mutlu B.
    Using free simplicial algebras with given CW−basis, it is shown how to construct a free or totally free quasi 3-crossed module on suitable construction data. Quasi 3-crossed complexes are introduced and similar freeness results are given for these are discussed. © 2013, Mutlu and Mutlu; licensee Springer.
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    Improved Jacobi matrix method for the numerical solution of Fredholm integro-differential-difference equations
    (Springer Medizin, 2016) Bahşı M.M.; Kurt Bahşı A.; Çevik M.; Sezer M.
    This study is aimed to develop a new matrix method, which is used an alternative numerical method to the other method for the high-order linear Fredholm integro-differential-difference equation with variable coefficients. This matrix method is based on orthogonal Jacobi polynomials and using collocation points. The improved Jacobi polynomial solution is obtained by summing up the basic Jacobi polynomial solution and the error estimation function. By comparing the results, it is shown that the improved Jacobi polynomial solution gives better results than the direct Jacobi polynomial solution, and also, than some other known methods. The advantage of this method is that Jacobi polynomials comprise all of the Legendre, Chebyshev, and Gegenbauer polynomials and, therefore, is the comprehensive polynomial solution technique. © 2016, The Author(s).
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    A numerical approach for a nonhomogeneous differential equation with variable delays
    (Springer Medizin, 2018) Özel M.; Tarakçı M.; Sezer M.
    In this study, we consider a linear nonhomogeneous differential equation with variable coefficients and variable delays and present a novel matrix-collocation method based on Morgan–Voyce polynomials to obtain the approximate solutions under the initial conditions. The method reduces the equation with variable delays to a matrix equation with unknown Morgan–Voyce coefficients. Thereby, the solution is obtained in terms of Morgan–Voyce polynomials. In addition, two test problems together with error analysis are performed to illustrate the accuracy and applicability of the method; the obtained results are scrutinized and interpreted by means of tables and figures. © 2018, The Author(s).
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    Pell–Lucas series approach for a class of Fredholm-type delay integro-differential equations with variable delays
    (Springer Medizin, 2021) Dönmez Demir D.; Lukonde A.P.; Kürkçü Ö.K.; Sezer M.
    In this study, a Pell–Lucas matrix-collocation method is used to solve a class of Fredholm-type delay integro-differential equations with variable delays under initial conditions. The method involves the basic matrix structures gained from the expansions of the functions at collocation points. Therefore, it performs direct and immediate computation. To test its advantage on the applications, some numerical examples are evaluated. These examples show that the method enables highly accurate solutions and approximations. Besides, the accuracy of the solutions and the validity of the method are checked via the residual error analysis and the upper bound error, respectively. Finally, the numerical results, such as errors and computation time, are compared in the tables and figures. © 2021, Islamic Azad University.
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    A compatible Hermite–Taylor matrix-collocation technique with convergence test for second-order partial integro-differential equations containing two independent variables with functional bounds
    (Springer Medizin, 2022) Yalçın E.; Sezer M.
    The aim of this study is to offer a compatible numerical technique to solve second-order linear partial integro-differential equations with variable (functional) bounds, including two independent variables, under the initial and/or boundary conditions by using hybrid Hermite and Taylor series. The method converts the presented integro-differential equation to a matrix equation including the unknown Hermite coefficients. Solving this matrix equation and applying the collocation method, the approximate solution of the problem is obtained in terms of the Hermite polynomials. Also, by means of an error estimation and convergence test related to residual functions, some examples to illustrate the accuracy and efficiency of the method are fulfilled; the obtained results are scrutinized and interpreted. All numerical computations have been performed on the computer programs. © 2021, Islamic Azad University.