Yazar "Yagmurlu, N. Murat" seçeneğine göre listele

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    Double Exp-Function Method for Multisoliton Solutions of The Tzitzeica-Dodd-Bullough Equation
    (Springer Heidelberg, 2016) Esen, Alaattin; Yagmurlu, N. Murat; Tasbozan, Orkun
    In this work, it is aimed to find one- and two-soliton solutions to nonlinear Tzitzeica-Dodd-Bullough (TDB) equation. Since the double exp-function method has been widely used to solve several nonlinear evolution equations in mathematical physics, we have also used it with the help of symbolic computation for solving the present equation. The method seems to be easier and more accurate thanks to the recent developments in the field of symbolic computation.
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    Finite difference method combined with differential quadrature method for numerical computation of the modified equal width wave equation
    (Wiley, 2021) Bashan, Ali; Yagmurlu, N. Murat; Ucar, Yusuf; Esen, Alaattin
    The aim of this study is to improve the numerical solution of the modified equal width wave equation. For this purpose, finite difference method combined with differential quadrature method with Rubin and Graves linearizing technique has been used. Modified cubic B-spline base functions are used as base function. By the combination of two numerical methods and effective linearizing technique high accurate numerical algorithm is obtained. Three main test problems are solved for various values of the coefficients. To observe the performance of the present method, the error norms of the single soliton problem which has analytical solution are calculated. Besides these error norms, three invariants are reported. Comparison of the results displays that our algorithm produces superior results than those given in the literature.
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    A mixed method approach to the solitary wave, undular bore and boundary-forced solutions of the Regularized Long Wave equation
    (Springer Heidelberg, 2022) Bashan, Ali; Yagmurlu, N. Murat
    The aim of the present work is to obtain numerical solutions of the solitary wave, undular bore and boundary-forced problems for Regularized Long Wave (RLW) equation. For this purpose, low-order modified cubic B-spline is chosen as base functions. Crank-Nicolson formulae combined with efficient space discretization method have been applied. With the aid of Rubin and Graves type linearization technique, nonlinear terms are linearized and a solvable linear equation system has been obtained. Three significant test problems in the literature are solved successfully. The present algorithm has obtained high accurate numerical solutions of the RLW equation. Numerical results are compared with those of some earlier ones and given. The rates of the convergence are also investigated.
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    A new perspective for quintic B-spline based Crank-Nicolson-differential quadrature method algorithm for numerical solutions of the nonlinear Schrodinger equation
    (Springer Heidelberg, 2018) Bashan, Ali; Ucar, Yusuf; Yagmurlu, N. Murat; Esen, Alaattin
    In the present paper, a Crank-Nicolson-differential quadrature method (CN-DQM) based on utilizing quintic B-splines as a tool has been carried out to obtain the numerical solutions for the nonlinear Schrodinger (NLS) equation. For this purpose, first of all, the Schrodinger equation has been converted into coupled real value differential equations and then they have been discretized using both the forward difference formula and the Crank-Nicolson method. After that, Rubin and Graves linearization techniques have been utilized and the differential quadrature method has been applied to obtain an algebraic equation system. Next, in order to be able to test the efficiency of the newly applied method, the error norms, L-2 and L-infinity, as well as the two lowest invariants, I-1 and I-2, have been computed. Besides those, the relative changes in those invariants have been presented. Finally, the newly obtained numerical results have been compared with some of those available in the literature for similar parameters. This comparison clearly indicates that the currently utilized method, namely CN-DQM, is an effective and efficient numerical scheme and allows us to propose to solve a wide range of nonlinear equations.
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    A new perspective for the numerical solutions of the cmKdV equation via modified cubic B-spline differential quadrature method
    (World Scientific Publ Co Pte Ltd, 2018) Bashan, Ali; Yagmurlu, N. Murat; Ucar, Yusuf; Esen, Alaattin
    In the present paper, a novel perspective fundamentally focused on the differential quadrature method using modifi ed cubic B-spline basis functions are going to be applied for obtaining the numerical solutions of the complex modified Korteweg-de Vries (cmKdV) equation. In order to test the effectiveness and effciency of the present approach, three test problems, that is single solitary wave, interaction of two solitary waves and interaction of three solitary waves will be handled. Furthermore, the maximum error norm L-infinity will be calculated for single solitary wave solutions to measure the effciency and the accuracy of the present approach. Meanwhile, the three lowest conservation quantities will be calculated and also used to test the effciency of the method. In addition to these test tools, relative changes of the invariants will be calculated and presented. In the end of these processes, those newly obtained numerical results will be compared with those of some of the published papers. As a conclusion, it can be said that the present approach is an effective and effcient one for solving the cmKdV equation and can also be used for numerical solutions of other problems.
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    A New Perspective on The Numerical Solution for Fractional Klein Gordon Equation
    (Gazi Univ, 2019) Karaagac, Berat; Ucar, Yusuf; Yagmurlu, N. Murat; Esen, Alaattin
    In the present manuscript, a new numerical scheme is presented for solving the time fractional nonlinear Klein-Gordon equation. The approximate solutions of the fractional equation are based on cubic B-spline collocation finite element method and L2 algorithm. The fractional derivative in the given equation is handled in terms of Caputo sense. Using the methods, fractional differential equation is converted into algebraic equation system that are appropriate for computer coding. Then, two model problems are considered and their error norms are calculated to demonstrate the reliability and efficiency of the proposed method. The newly calculated error norms show that numerical results are in a good agreement with the exact solutions.
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    Numerical approximation to the MEW equation for the single solitary wave and different types of interactions of the solitary waves
    (Taylor & Francis Ltd, 2022) Bashan, Ali; Ucar, Yusuf; Yagmurlu, N. Murat; Esen, Alaattin
    The main motivation of the current study is to find out better approximate solutions of the modified equal width wave (MEW) equation. In order to achieve this aim, the power of two numerical methods are combined and an extended literature survey has been carried out. Quartic B-spline base functions have been utilized since the first-order and second-order weighting coefficients that are needed for space discretization are obtained directly. As test problems, twelve different applications of single solitary wave and four different applications of the interaction between the two solitary waves are solved successfully. All of the approximate solutions have been compared to nearly fifty various earlier applications existing in the literature. Also, the rate of the convergence is given with error norms. Comparisons show the fact that the current method obtains improved results than most of the common earlier methods.
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    Numerical solution of the complex modified Korteweg-de Vries equation by DQM
    (Iop Publishing Ltd, 2016) Bashan, Ali; Ucar, Yusuf; Yagmurlu, N. Murat; Esen, Alaattin
    In this paper, a method based on the differential quadrature method with quintic B-spline has been applied to simulate the solitary wave solution of the complex modified Kortewegde Vries equation (CMKdV). Three test problems, namely single solitary wave, interaction of two solitary waves and interaction of three solitary waves have been investigated. The efficiency and accuracy of the method have been measured by calculating maximum error norm L-infinity for single solitary waves having analytical solutions. Also, the three lowest conserved quantities and obtained numerical results have been compared with some of the published numerical results.
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    NUMERICAL SOLUTIONS AND STABILITY ANALYSIS OF MODIFIED BURGERS EQUATION VIA MODIFIED CUBIC B-SPLINE DIFFERENTIAL QUADRATURE METHODS
    (Yildiz Technical Univ, 2019) Ucar, Yusuf; Yagmurlu, N. Murat; Bashan, Ali
    The purpose of this work is obtain the numerical approximate solutions of the nonlinear modified Burgers' equation (MBE) via the modified cubic B-spline (MCB) differential quadrature methods (DQMs). The accuracy and effectiveness of the methods are measured and reported by finding out error normsL(2) and L-infinity. The present numerical results have been compared with some earlier studies and this comparison clearly indicates that the method is an outstanding numerical scheme for the solution of the MBE. A stability analysis has at the same time been given.
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    NUMERICAL SOLUTIONS FOR THE FOURTH ORDER EXTENDED FISHER-KOLMOGOROV EQUATION WITH HIGH ACCURACY BY DIFFERENTIAL QUADRATURE METHOD
    (Yildiz Technical Univ, 2018) Bashan, Ali; Ucar, Yusuf; Yagmurlu, N. Murat; Esen, Alaattin
    In this paper, modified cubic B-spline based differential quadrature method (MCB-DQM) has been used to obtain the numerical solutions for the fourth order extended Fisher-Kolmogorov equation (EFK). After using DQM for discretization of the EFK equation, ordinary differential equation systems have been obtained. For time integration, strong stability preserving Runge-Kutta method has been used. Numerical solutions of the three test problems have been investigated. The efficiency and accuracy of the method have been measured by calculating error norms L-2 and L-infinity. The present obtained numerical results have been compared with the published numerical results and the comparison has shown that the method is an effective numerical scheme to solve the EFK equation.
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    Numerical Solutions of the Modified Burgers Equation by a Cubic B-spline Collocation Method
    (Springer, 2016) Kutluay, Selcuk; Ucar, Yusuf; Yagmurlu, N. Murat
    In this paper, a numerical solution of the modified Burgers equation is obtained by a cubic B-spline collocation method. In the solution process, a linearization technique based on quasi-linearization has been applied to deal with the non-linear term appearing in the equation. The computed results are compared with others selected from the available literature. The error norms and are computed and found to be sufficiently small. A Fourier stability analysis of the method is also investigated.
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    A study on the improved tan(? (?)/2) -expansion method
    (E D P Sciences, 2017) Karaagac, Beret; Yagmurlu, N. Murat; Esen, Alaattin
    In this study, the improved tan(phi(xi) /2) -expansion method (ITEM), one of the improved expansion methods, has been applied to (3+1)- dimensional Jimbo Miwa and Sharma-Tasso-Olver equations using symbolic computation. With the aid of the method, many new and abundant analytical solutions have been obtained. The newly obtained results show that ITEM is a new and significant technique for solving nonlinear differential equations which plays an important role on fluids mechanics, engineering and many physics fields.