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    A finite element approach for solution of Burgers' equation
    (Elsevier Science Inc, 2003) Özis, T; Aksan, EN; Özdes, A
    In this study, for the Burgers' equation which is used a model problem in turbulence and shock wave theory was given a finite element solution. Considering the numerical results obtained for different values of viscosity compared with Cole's analytical solution, it was seen that they were in good agreement. (C) 2002 Published by Elsevier Science Inc.
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    Numerical solution of Burgers' equation by quadratic B-spline finite elements
    (Elsevier Science Inc, 2005) Özis, T; Esen, A; Kutluay, S
    In this paper, a Galerkin quadratic B-spline finite element method is used to solve numerically the one-dimensional Burgers' equation reduced by the Hopf-Cole transformation. The performance of the method is tested on two model problems involving moderately Reynolds numbers with known exact solutions. The obtained numerical results show that the method is efficient, robust and reliable for solving Burgers' equation accurately even involving high Reynolds numbers for which the exact solution fails. Computed results are compared with other numerical results in the literature. A stability analysis of the method is also investigated. (c) 2004 Elsevier Inc. All rights reserved.
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    A simple similarity-transformation-iterative scheme applied to Korteweg-de Vries equation
    (Elsevier Science Inc, 2006) Özis, T; Özer, S
    In this paper, we apply a simple iterative scheme and give an algorithm to solve the reduced Korteweg-de Vries equation by a scaled similarity-transformation. The obtained numerical solutions are valid for the whole solution domain. Results obtained by the method have been compared with the solution of Marchant and Smyth [T.R. Marchant, N.F. Smyth, Initial-boundary value problems for the KdV equations, IMA J. Appl. Math. 47 (1991) 247-264] and are found to be in good agreement with each other. (c) 2005 Elsevier Inc. All rights reserved.