Yazar "Düz, Murat" seçeneğine göre listele

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    An alternative method to undetermined coefficients method with aid of fourier transform
    (2018) Düz, Murat
    In this paper, The Fourier transforms studied for special solution of ordinary differential equations. These equations of which right sideis in the form $eaxPm(x)$, where $ Pm(x) $is a polnomial from m.th degree, are nonhomogeneous constant coeffients. With this method wecan solve all the equations that can be solved by the method of undeterminated coefficients.That is, this method is an alternative tothe undetermined coefficients method.
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    On Solution of complex equations with the homotopy perturbation method
    (Adiyaman University, 2024-12-31) Düz, Murat; Çamlica, Şeyda
    In this study, complex differential equations are solved using the homotopy perturbation method (HPM). Firstly, we separated the real and imaginary parts of the equation. Thus, from one unknown equation is obtained two unknown equation systems. Later, we applied HPM real and imaginary to parts of the equation. So, we have obtained real and imaginary parts of the solution.
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    On the existence and uniqueness of solutions of a certain class of non-linear singular integral equations
    (2011) Düz, Murat
    In this study, the existence of a solution of the non-linear singular integral equation system$w(z) = f1 \\biggl ( z,w(z),h(z), T_G g_1(· ,w(·), h(·))(z)$, $. \\hspace{40mm} \\Pi_Gg_1(· ,w(·), h(·))(z) \\biggr )$, $h(z) = f_2 \\biggl ( z,w(z), h(z), T_Gg_2(·,w(·), h(·))(z)$,$. \\hspace{40mm} \\Pi_Gg_2(· ,w(·), h(·))(z) \\biggr )$ , has been investigated. This system is more general than the one$w(z) = f_1 (z,w(z), h(z), T_Gg_1(· ,w(·), h(·))(z))$, $h(z) = f_2 (z,w(z), h(z),\\Pi_Gg_2(·,w(·), h(·)) (z))$,studied by Musayev and Duz (Existence and uniqueness theorems for a certain class of non linear singular integral equations SJAM 10 (1), 3– 18, 2009). Here, $T_Gf(z)$ and $\\Pi_Gf(z) are the Vekua integral operators defined by $T_Gf(z)=- \\frac{1}{\\pi} \\int_G \\int \\frac{f(\\varsigma)}{\\varsigma - z} d\\xi d\\eta$, $\\Pi_Gf(z)=- \\frac{1}{\\pi} \\int_G \\int \\frac{f(\\varsigma)}{(\\varsigma - z)^2} d\\xi d\\eta$.
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    Solution of lane-emden equation with fourier decomposition method
    (2022) Düz, Murat
    In this article, we tried to get the solution of a class of Lane Emden type equations by using the Fourier Decomposition Method. This method is obtained by using the Fourier transform and the Adomian Decomposition method (FADM) together.
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    Solution of n.th order constant coefficients complex partial derivative equations by using fourier transform method
    (2020) Düz, Murat
    The aim of this article is to find a specific solution for constant coefficients complex partial differential equations using Fourier transform. Firstly, equality of complex derivatives have been obtained from kind real derivatives. Later Fourier Transforms have been used for obtained equation. Finally a formula has been given for a special solution of these kind equations. Also, examples are given to display the validity of the present method.
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    Solutions to differential-differential difference equations with variable coefficients by using fourier transform method
    (2023) Düz, Murat; Avezov, Sunnet; Issa, Ahmad
    In this paper, differential-differential difference equations with variable coefficients have been solved using the Fourier Transform Method (FTM). In addition, new definitions and theorems are introduced. Besides, the efficiency of the proposed method is verified by solving five important examples. Furthermore, we have noted that the Fourier transform method is a powerful technique for solving ordinary differential difference equations (ODDEs) with variable coefficients. It involves transforming the ODDEs into the frequency domain using the Fourier transform, solving the transformed equation, and then applying the inverse Fourier transform to obtain the solution in the time domain.