Solitary waves of the splitted RLW equation Original Research Article

A combination of the splitting method and the cubic B-spline finite elements is used to solve the non-linear regularized long wave (RLW) equation. This approach involves a Bubnov–Galerkin method with cubic B-spline finite elements so that there is continuity of the dependent variable and its first derivative throughout the solution region. Time integration of the resulting systems is effected using a Crank–Nicholson approximation. In simulations of the migration of a single solitary wave this algorithm is shown to have higher accuracy and better conservation than a recent splitting difference scheme based on cubic spline interpolation functions, for different amplitudes ranging from a very small (⩾0.03) to a considerably high amplitudes (⩽0.3). The development of an undular bore is modeled.