Asif Yokus

A numerical comparison of partial solutions in the decomposition method for linear and nonlinear partial differential equations

In this study, the decomposition method for solving the linear heat equation and nonlinear Burgers equation is implemented with appropriate initial conditions. The application of the method demonstrated that the partial solution in the x-direction requires more computational work when compared with the partial solution developed in the t-direction but the numerical solution in the x-direction are performed extremely well in terms of accuracy and efficiency.

A decomposition method for finding solitary and periodic solutions for a coupled higher-dimensional Burgers equations

In this paper, we consider coupled higher-dimensional Burgers (chdBur) equations. We find periodic solutions to chdBur equations using a modified Adomians decomposition method (mADM). We find both exact and numerical solutions. We compared the numerical solutions with corresponding analytical solutions. We also show the effectiveness of the method.

An application of a new version of (G′/G)-expansion method

In this study, we develop extended (G′/G)-expansion method which is suggested in [1]. By this method, we find traveling wave solutions of nonlinear KdV and Hirota-Satsuma equations.In this study, we develop extended (G′/G)-expansion method which is suggested in [1]. By this method, we find traveling wave solutions of nonlinear KdV and Hirota-Satsuma equations.

Conservation laws and a new expansion method for sixth order Boussinesq equation

In this study, we analyze the conservation laws of a sixth order Boussinesq equation by using variational derivative. We get sixth order Boussinesq equation’s traveling wave solutions with (1/G) −expansion method which we constitute newly by being inspired with (G/G) −expansion method which is suggested in [1]. We investigate conservation laws of the analytical solutions which we obtained by the new constructed method. The analytical solution’s conductions which we get according to new expansion method are given graphically.

Numerical solutions of Fisher’s equation with collocation method

In this paper, the collocation method using radial basis functions is presented for a numerical solution of Fisher’s equation. In the solution process, we use linearization techniques for non-linear term existing in the equation. Furthermore, the methods which are analyzed by the error norms L2 and L∞ and by matrix stability analysis are tested for numerical examples and results obtained by four radial basis functions from computer runs are compared.