Ozlem Ersoy

Alper Korkmaz, Ozlem Ersoy, Idiris Dag

Occupation of an interval by self-replicating initial pulses is studied numerically. Two different approximates in different categories are proposed for the numerical solutions of some initial-boundary value problems. The sinc differential quadrature combined with third-fourth order implicit Rosenbrock and exponential B-spline collocation methods are setup to obtain the numerical solutions of the mentioned problems. The numerical simulations containing occupation of single initial pulse, non or slow occupation model and covering the domain with two initial pulses are demonstrated by using both proposed methods.

Ozlem Ersoy, Idris Dag

In this study, we set up a numerical technique to get approximate solutions of Fisher's equation which is one of the most important model equation in population biology. We integrate the equation fully by using combination of the trigonometric cubic B-spline functions for space variable and Crank-Nicolson for the time integration. Numerical results have been presented to show the accuracy of the current algorithm. We have seen that the proposed technique is a good alternative to some existing techniques for getting solutions of the Fisher's equation.

Ozlem Ersoy, Idris Dag, Ali Sahin

In this paper, we investigate the numerical solutions of the cubic nonlinear Schrodinger equation via the exponential B-spline collocation method. Crank-Nicolson formulas are used for time discretization of the target equation. A linearization technique is also employed for the numerical purpose. Four numerical examples related to single soliton, collision of two solitons that move in opposite directions, the birht of standing and mobile solitons and bound state solution are considered as the test problems. The accuracy and the efficiency of the purposed method are measured by max error norm and conserved constants. The obtained results are compared with the possible analytical values and those in some earlier studies.

Ozlem Ersoy, Idiris Dag, Alper Korkmaz

In the study, the collocation method based on exponential cubic B-spline functions is proposed to solve one dimensional Boussinesq systems numerically. Two initial boundary value problems for Regularized and Classical Boussinesq systems modeling motion of traveling waves are considered. The accuracy of the method is validated by measuring the error between the numerical and analytical solutions. The numerical solutions obtained by various values of free parameter $p$ are compared with some solutions in literature.

Ozlem Ersoy, Idris Dag

The coupled Burgers equation is solved by way of the trigonometric B-spline collocation method. The unknown of the coupled Burgers equation is integrated in time by aid of the Crank-Nicolson method. Resulting time-integrated coupled Burgers equation is discretized using the trigonometric cubic B-spline collocation method. Fully-integrated couupled Burgers equation which is a system of nonlinear algebraic equation is solved with a variant of Thomas algorithm. The three model test problems are studied to illustrate the accuracy of the suggested method.

Ozlem Ersoy, Idris Dag, Nihat Adar

The exponential cubic B-spline functions are used to set up the collocation method for finding solutions of the Burgers's equation. The effect of the exponential cubic B-splines in the collocation method is sought by studying four text problems.

Ozlem Ersoy, Idiris Dag

The exponential cubic B-spline functions together with Crank Nicolson are used to solve numerically the nonlinear coupled Burgers' equation using collocation method. This method has been tested by three different problems. The proposed scheme is compared with some existing methods. We have noticed that proposed scheme produced a highly accurate results.