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Öğe ALTERNATING DIRECTION IMPLICIT METHOD FOR NUMERICAL SOLUTIONS OF 2-D BURGERS EQUATIONS(Vinca Inst Nuclear Sci, 2019) Celikten, Gonca; Aksan, Emine NesligulIn this study, the system of 2-D Burgers equations is numerically solved by using alternating direction implicit method. Two model problems are studied to demonstrate the efficiency and accuracy of the alternating direction implicit method. Numerical results obtained by present method are compared with the exact solutions and numerical solutions given by other researchers. It is displayed that the method is unconditionally stable by using the von-Neumann (Fourier) stability analysis method. It is shown that all results are in good agreement with the results given by existing numerical methods in the literature.Öğe AN APPLICATION OF CUBIC B-SPLINE FINITE ELEMENT METHOD FOR THE BURGERS' EQUATION(Vinca Inst Nuclear Sci, 2018) Aksan, Emine NesligulIt is difficult to achieve exact solution of non-linear PDE, directly. Sometimes, it is possible to convert non-linear PDE into equivalent linear PDE by applying a convenient transformation. Hence, Burgers' equation replaces with heat equation by means of the Hope-Cole transformation. In this study, Burgers' equation was converted to a set of non-linear ODE by keeping non-linear structure of Burgers' equation. In this case, solutions for each of the non-linear ODE were obtained by the help of the cubic B-spline finite element method. Model problems were considered to verify the efficiency of this method. Agreement of the solutions was shown with graphics and tables.Öğe AN APPLICATION OF FINITE ELEMENT METHOD FOR A MOVING BOUNDARY PROBLEM(Vinca Inst Nuclear Sci, 2018) Aksan, Emine Nesligul; Karabenli, Hatice; Esen, AlaattinThe Stefan problems called as moving boundary problems are defined by the heat equation on the domain 0 < x < s(t). In these problems, the position of moving boundary s(t) is determined as part of the solution. As a result, they are non-linear problems and thus have limited analytical solutions. In this study, we are going to consider a Stefan problem described as solidification problem. After using variable space grid method and boundary immobilization method, collocation finite element method is applied to the model problem. The numerical solutions obtained for the position of moving boundary are compared with the exact ones and the other numerical solutions existing in the literature. The newly obtained numerical results are more accurate than the others for the time step Delta t = 0.0005, it is also seen from the tables, the numerical solutions converge to exact solutions for the larger element numbers.Öğe New solitary wave structures to the (3(Elsevier, 2019) Bulut, Hasan; Aksan, Emine Nesligul; Kayhan, Mirac; Sulaiman, Tukur AbdulkadirThe studies of the dynamic behaviors of nonlinear models arising in ocean engineering play a significant role in our daily activities. In this paper, an efficient mathematical technique, namely; the sine-Gordon expansion method is employed to construct the traveling wave solutions to the (3 + 1)-dimensional Kadomtsev-Petviashvili and (3 + 1)-dimensional nonlinear Schrodinger equations. Using suitable values of the parameters, the two- and three-dimensional figures of the obtained solutions are plotted. (C) 2019 Shanghai Jiaotong University. Published by Elsevier B.V.Öğe Some Wave Simulation Properties of the (2+1) Dimensional Breaking Soliton Equation(E D P Sciences, 2017) Aksan, Emine Nesligul; Bulut, Hason; Kayhan, MiracIn this paper, we apply an efficient method which is improved Bernoulli sub-equation function method (IBSEFM) to (2+1) dimensional Breaking Soliton equation. It gives some new wave simulations like complex and exponential structures. We test whether all structures verify the (2+1) dimensional Breaking Soliton model. Then, we draw three and two dimensional plane by using Wolfram Mathematica 9.
