Yazar "Yagmurlu, N. M." seçeneğine göre listele

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    Approximate Analytical Solution to Time-Fractional Damped Burger and Cahn-Allen Equations
    (Natural Sciences Publishing Corp-Nsp, 2013) Esen, A.; Yagmurlu, N. M.; Tasbozan, O.
    The aim of the present paper is to obtain the approximate analytical solutions of time-fractional damped burger and Cahn-Allen equations by means of the homotopy analysis method (HAM). In the HAM solution, there exists an auxiliary parameter (h) over bar which provides a convenient way to adjust and check the convergence region of the solution series. In the model problems, an appropriate choice of the auxiliary parameter has been examined for increasing values of time.
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    A B-spline collocation method for solving fractional diffusion and fractional diffusion-wave equations
    (Tbilisi Centre Math Sci, 2015) Esen, A.; Tasbozan, O.; Ucar, Y.; Yagmurlu, N. M.
    In this paper,we have considered the fractional diffusion and fractional diffusion wave equations in which the time derivative is a fractional derivative in the Caputo form and have obtained their numerical solutions by collocation method using cubic B-spline base functions. In the solution process, for the fractional diffusion equation L1 discretizaton formula of the fractional derivative is applied, and for the fractional diffusion-wave equation L2 discretizaton formula of the fractional derivative is applied. Accuracy of the proposed method is discussed by computing the error norms L2 and L-infinity. A stability analysis of the approximation obtained by the scheme shows that the method is unconditionally stable.
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    A Numerical Solution to Fractional Diffusion Equation for Force-Free Case
    (Hindawi Ltd, 2013) Tasbozan, O.; Esen, A.; Yagmurlu, N. M.; Ucar, Y.
    A collocation finite element method for solving fractional diffusion equation for force-free case is considered. In this paper, we develop an approximation method based on collocation finite elements by cubic B-spline functions to solve fractional diffusion equation for force-free case formulated with Riemann-Liouville operator. Some numerical examples of interest are provided to show the accuracy of the method. A comparison between exact analytical solution and a numerical one has been made.
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    Numerical Solutions of the Modified Burgers' Equation by Finite Difference Methods
    (De Gruyter Poland Sp Zoo, 2017) Ucar, Y.; Yagmurlu, N. M.; Tasbozan, O.
    In this study, a numerical solution of the modified Burgers' equation is obtained by the finite difference methods. For the solution process, two linearization techniques have been applied to get over the non-linear term existing in the equation. Then, some comparisons have been made between the obtained results and those available in the literature. Furthermore, the error norms L-2 and L-infinity are computed and found to be sufficiently small and compatible with others in the literature. The stability analysis of the linearized finite difference equations obtained by two different linearization techniques has been separately conducted via Fourier stability analysis method.