The aim of the present paper is to present a numerical algorithm for the time-dependent generalized regularized long wave equation with boundary conditions. We semi-discretize the continuous problem by means of the Cr...The aim of the present paper is to present a numerical algorithm for the time-dependent generalized regularized long wave equation with boundary conditions. We semi-discretize the continuous problem by means of the Crank-Nicolson finite difference method in the temporal direction and exponential B-spline collocation method in the spatial direction. The method is shown to be unconditionally stable. It is shown that the method is convergent with an order of θ（k2 ＋ h2）. Our scheme leads to a tri-diagonal nonlinear system. This new method has lower computational cost in comparison to the Sinc-collocation method. Finally, numerical examples demonstrate the stability and accuracy of this method.展开更多
By using modified simple equation method,we study the generalized RLW equation and symmetric RLW equation,the subsistence of solitary wave,periodic cusp wave,periodic bell wave solutions are obtained.We establish some...By using modified simple equation method,we study the generalized RLW equation and symmetric RLW equation,the subsistence of solitary wave,periodic cusp wave,periodic bell wave solutions are obtained.We establish some conditions on the parameters for which the obtained solutions are dark or bright soliton.The proficiency of the methods for constructing exact solutions has been established.Finally,the variety of structure and graphical representation makes the dynamics of the equations visible and provides the mathematical foundation in shallow water,plasma and ion acoustic plasma waves.展开更多
文摘The aim of the present paper is to present a numerical algorithm for the time-dependent generalized regularized long wave equation with boundary conditions. We semi-discretize the continuous problem by means of the Crank-Nicolson finite difference method in the temporal direction and exponential B-spline collocation method in the spatial direction. The method is shown to be unconditionally stable. It is shown that the method is convergent with an order of θ（k2 ＋ h2）. Our scheme leads to a tri-diagonal nonlinear system. This new method has lower computational cost in comparison to the Sinc-collocation method. Finally, numerical examples demonstrate the stability and accuracy of this method.
文摘By using modified simple equation method,we study the generalized RLW equation and symmetric RLW equation,the subsistence of solitary wave,periodic cusp wave,periodic bell wave solutions are obtained.We establish some conditions on the parameters for which the obtained solutions are dark or bright soliton.The proficiency of the methods for constructing exact solutions has been established.Finally,the variety of structure and graphical representation makes the dynamics of the equations visible and provides the mathematical foundation in shallow water,plasma and ion acoustic plasma waves.
