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    Operator splitting for numerical solution of the modified Burgers' equation using finite element method
    (Wiley, 2019) Ucar, Yusuf; Yagmurlu, Nuri M.; Celikkaya, Ihsan
    The aim of this study is to obtain numerical behavior of a one-dimensional modified Burgers' equation using cubic B-spline collocation finite element method after splitting the equation with Strang splitting technique. Moreover, the Ext4 and Ext6 methods based on Strang splitting and derived from extrapolation have also been applied to the equation. To observe how good and effective this technique is, we have used the well-known the error norms L-2 and in the literature and compared them with previous studies. In addition, the von Neumann (Fourier series) method has been applied after the nonlinear term has been linearized to investigate the stability of the method.
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    OPERATOR SPLITTING FOR NUMERICAL SOLUTIONS OF THE RLW EQUATION
    (Wilmington Scientific Publisher, Llc, 2018) Yagmurlu, Nuri Murat; Ucar, Yusuf; Celikkaya, Ihsan
    In this study, the numerical behavior of the one-dimensional Regularized Long Wave (RLW) equation has been sought by the Strang splitting technique with respect to time. For this purpose, cubic B-spline functions are used with the finite element collocation method. Then, single solitary wave motion, the interaction of two solitary waves and undular bore problems have been studied and the effectiveness of the method has been investigated. The new results have been compared with those of some of the previous studies available in the literature. The stability analysis has also been taken into account by the von Neumann method.
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    Operator splitting method for numerical solution of modified equal width equation
    (Tbilisi Centre Math Sci, 2019) Celikkaya, Ihsan
    In this manuscript, numerical solutions of the equations in the form of u(t) = Au + B(u) have been sought for, where A and B are linear and nonlinear operators, respectively. The modified equal width (MEW) equation has been converted into two sub problems. Then, the sub problems were solved according to the Strang splitting scheme by applying the cubic B-spline collocation finite element method. Thus, more accurate results of the equation MEW have been obtained than those non-splitting users. In order to test the accuracy and efficiency of the present method; single soliton, interaction of two solitons and Maxwellian initial condition pulse problems have been considered. Moreover, the stability analysis of each sub problem has been investigated by von-Neumann analysis method.