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Öğe A finite difference solution of the regularized long-wave equation(Hindawi Ltd, 2006) Kutluay, S.; Esen, A.A linearized implicit finite difference method to obtain numerical solution of the one-dimensional regularized long-wave (RLW) equation is presented. The performance and the accuracy of the method are illustrated by solving three test examples of the problem: a single solitary wave, two positive solitary waves interaction, and an undular bore. The obtained results are presented and compared with earlier work.Öğe The (G?/G)-expansion method for some nonlinear evolution equations(Elsevier Science Inc, 2010) Kutluay, S.; Esen, A.; Tasbozan, O.In this paper, the (G'G)-expansion method is applied to the Liouville, sine-Gordon and new coupled MKdV equations to obtain their some generalized exact travelling wave solutions. (C) 2010 Elsevier Inc. All rights reserved.Öğe A Numerical Approach to the Rosenau-KdV equation using Galerkin Cubic Finite Element Method(Centre Environment Social & Economic Research Publ-Ceser, 2017) Ucar, Y.; Karaagac, B.; Kutluay, S.In this paper, a Galerkin finite element method has been used to solve numerically the Rosenau-KdV equation using cubic B-spline functions. The system of ordinary differential equations obtained in terms of element parameters by the application of the method has been solved by using the fourth order Runge-Kutta method. The error norms L-2 and L-infinity together with invariants I-1 and I-2 have been calculated to show the accuracy and efficiency of the method. The computed results have been compared with exact values and also other numerical results available in the literature.Öğe Numerical solution of a coupled modified Korteweg-de Vries equation by the Galerkin method using quadratic B-splines(Taylor & Francis Ltd, 2013) Kutluay, S.; Ucar, Y.In this paper, numerical solutions of a coupled modified Korteweg-de Vries equation have been obtained by the quadratic B-spline Galerkin finite element method. The accuracy of the method has been demonstrated by five test problems. The obtained numerical results are found to be in good agreement with the exact solutions. A Fourier stability analysis of the method is also investigated.Öğe Numerical solutions of the coupled Burgers' equation by the Galerkin quadratic B-spline finite element method(Wiley, 2013) Kutluay, S.; Ucar, Y.In this paper, a coupled Burgers' equation has been numerically solved by a Galerkin quadratic B-spline FEM. The performance of the method has been examined on three test problems. Results obtained by the method have been compared with known exact solution and other numerical results in the literature. A Fourier stability analysis of the method is also investigated. Copyright (c) 2013 John Wiley & Sons, Ltd.Öğe Solitary wave solutions of the modified equal width wave equation(Elsevier Science Bv, 2008) Esen, A.; Kutluay, S.In this paper we use a linearized numerical scheme based on finite difference method to obtain solitary wave solutions of the one-dimensional modified equal width (MEW) equation. Two test problems including the motion of a single solitary wave and the interaction of two solitary waves are solved to demonstrate the efficiency of the proposed numerical scheme. The obtained results show that the proposed scheme is an accurate and efficient numerical technique in the case of small space and time steps. A stability analysis of the scheme is also investigated. (c) 2006 Elsevier B.V. All rights reserved.
