In the present study, the Modified Equal Width (MEW) wave equation is going to be solved numerically by presenting a new technique based on collocation finite element method in which trigonometric cubic B-splines are used as approximate functions. In order to support the present study, three test problems; namely, the motion of a single solitary wave, interaction of two solitary waves and the birth of solitons are studied. The newly obtained results are compared with some of the other published numerical solutions available in the literature. The accuracy of the proposed method is discussed by computing the numerical conserved laws as well as the error norms L₂ and L_{∞}.

In the present article, the numerical simulation of the two-dimensional coupled Burgers equation (2D-cBE) has been sought by finite difference method based on Crank-Nicolson type approximation Widely used three test examples given with appropriate initial and boundary conditions are used for the simulation process. During the simulation process,the error norms L₂, L_{∞} are calculated if the exact solutions are already known, otherwise the pointwise values and graphics are provided for comparison. The newly obtained error norms L₂, L_{∞} by the presented schemes are compared with those of some of the numerical solutions in the literature. A good consistency and accuracy are observed both by numerical values and visual illustrations.

In the present study, the coupled Burgers’ equation is going to be solved numerically by presenting a new technique based on collocation finite element method in which trigonometric cubic and quintic B-splines are used as approximate functions. In order to support the present study, three test problems given with appropriate initial and boundary conditions are studied. The newly obtained results are compared with some of the other published numerical solutions available in the literature. The accuracy of the proposed method is discussed by computing the error norms L₂ and L_{∞}. A linear stability analysis of the approximation obtained by the scheme shows that the method is unconditionally stable.

The basic idea of this article is to investigate the numerical solutions of Gardner Kawahara equation, a particular case of extended Korteweg-de Vries (KdV) equation, by means of finite element method.