The boundary-forced regularised long-wave equation.

The regularised long-wave equation is solved numerically by a B-spline finite-element method involving a Galerkin approach with cubic B-spline finite-elements so that the dependent variable and its first derivative are continuous throughout the solution range. Time integration of the resulting system of ordinary differential equations is effected using a Crank-Nicolson approximation. The numerical scheme is validated by studying the motion of a single solitary wave. The amplitude, velocity and position of the wave are well represented and the method shows good conservation. The effect of inhomogeneous boundary conditions on the numerical solution is explored, and found to result in the establishment of a source of solitary waves.