Exponential B-spline collocation method for numerical solution of the generalized regularized long wave equation

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 O(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.