Yazar "Kurnaz, Aydin" seçeneğine göre listele

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    Adomian decomposition method by Gegenbauer and Jacobi polynomials
    (TAYLOR & FRANCIS LTD, 2011) Cenesiz, Yucel; Kurnaz, Aydin
    In this paper, orthogonal polynomials on [-1,1] interval are used to modify the Adomian decomposition method (ADM). Gegenbauer and Jacobi polynomials are employed to improve the ADM and compared with the method of using Chebyshev and Legendre polynomials. To show the efficiency of the developed method, some linear and nonlinear examples are solved by the proposed method, results are compared with other modifications of the ADM and the exact solutions of the problems.
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    An Efficient Approach for Solving Telegraph Equation
    (AMER INST PHYSICS, 2015) Koc, Ayse Betul; Kurnaz, Aydin
    In this study, a new numerical scheme for the solution of one dimensional telegraph equationis investigated. The approximate solutions are obtained in the form of the truncated Fibonacci type bivariate series. By means of the proposed method, quite effective results for the partial differential equations defined on the domain of Omega = {(x,y) : (x,y) is an element of[a,b] x [c,d] subset of R x R} can be obtained. An illustrative example is shown in order to clarify the findings of the approach. The results indicate that this method not only provide straightforward applicability and computational simplicity in the solution procedure, also achieve the validity.
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    A Matrix Method Based on the Fibonacci Polynomials to the Generalized Pantograph Equations with Functional Arguments
    (HINDAWI LTD, 2014) Koc, Ayse Betul; Cakmak, Musa; Kurnaz, Aydin
    A pseudospectral method based on the Fibonacci operational matrix is proposed to solve generalized pantograph equations with linear functional arguments. By using this method, approximate solutions of the problems are easily obtained in form of the truncated Fibonacci series. Some illustrative examples are given to verify the efficiency and effectiveness of the proposed method. Then, the numerical results are compared with other methods.
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    A new analytical approximate method for the solution of fractional differential equations
    (TAYLOR & FRANCIS LTD, 2008) Oturanc, Galip; Kurnaz, Aydin; Keskin, Yildiray
    A new analytical approximate method for the solution of fractional differential equations is presented. This method, which does not require any symbolic computation, is important as a tool for scientists and engineers because it provides an iterative procedure for obtaining the solution of both linear and non-linear fractional differential equations. The effectiveness of the proposed method is illustrated with some examples.
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    A new Fibonacci type collocation procedure for boundary value problems
    (SPRINGEROPEN, 2013) Koc, Ayse Betul; Cakmak, Musa; Kurnaz, Aydin; Uslu, Kemal
    In this study, we present a new procedure for the numerical solution of boundary value problems. This approach is mainly founded on the Fibonacci polynomial expansions, the so-called pseudospectral methods with the collocation method. The applicability and effectiveness of our proposed approach is shown by some illustrative examples. Then, the results indicate that this method is very effective and highly promising for linear differential equations defined on any subinterval of the real domain. MSC: 35A25.
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    A new kind of double Chebyshev polynomial approximation on unbounded domains
    (SPRINGEROPEN, 2013) Koc, Ayse Betul; Kurnaz, Aydin
    In this study, a new solution scheme for the partial differential equations with variable coefficients defined on a large domain, especially including infinities, has been investigated. For this purpose, a spectral basis, called exponential Chebyshev (EC) polynomials, has been extended to a new kind of double Chebyshev polynomials. Many outstanding properties of those polynomials have been shown. The applicability and efficiency have been verified on an illustrative example.
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    The solution of the Bagley-Torvik equation with the generalized Taylor collocation method
    (PERGAMON-ELSEVIER SCIENCE LTD, 2010) Cenesiz, Yuecel; Keskin, Yildiray; Kurnaz, Aydin
    In this paper, the Bagley-Torvik equation, which has an important role in fractional calculus, is solved by generalizing the Taylor collocation method. The proposed method has a new algorithm for solving fractional differential equations. This new method has many advantages over variety of numerical approximations for solving fractional differential equations. To assess the effectiveness and preciseness of the method, results are compared with other numerical approaches. Since the Bagley-Torvik equation represents a general form of the fractional problems, its solution can give many ideas about the solution of similar problems in fractional differential equations. (C) 2009 The Frankl in Institute. Published by Elsevier Ltd. All rights reserved.