THE BOUNDARY-FORCED REGULARIZED 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-spli ne finite-elements so that the dependent variable and its first deriva tive are continuous throughout the solution range. Time integration of the resulting system of ordinary differential equations is effected u sing a Crank-Nicolson approximation. The numerical scheme is validated by studying the motion of a single solitary wave. The amplitude, velo city and position of the wave are well represented and the method show s good conservation. The effect of inhomogeneous boundary conditions o n the numerical solution is explored, and found to result in the estab lishment of a source of solitary waves.