Ozlem Ersoy Hepson

Finite Element Method for Schnakenberg Model

In the study, solution of an initial boundary value problem for the Schnakenberg reaction-diffusion model is considered in numerical meaning. The approximate solution is assumed to be a finite series, some of exponential form of the cubic B-spline basis. After adapting the boundary data, the system is integrated in time variable by using Crank-Nicolson implicit method. The resultant iteration algorithm is initiated by the aid of the initial data adaption. The numerical results are compared with the analytical solution by using the relative error calculation that measures the ratio of the difference in the two successive time levels to the previous time level to validate the accuracy and the reliability.

Hyperbolic tangent solution to the conformable time fractional Zakharov-Kuznetsov equation in 3D space

In the study, hyperbolic tangent (tanh) ansatz solution is investigated for the conformable time fractional Zakharov-Kuznetsov Equation (fZKE) in 3D space. Transformation of the fZKE to an ODE by the compatible wave transformation is the first step of the methodology. It is assumed that there exists a solution of positive integer power of hyperbolic tangent form. Determining the power of the predicted solution follows some algebra to find the relations among the other parameters given in the solution. The final step is transforming the solution into original variables.