Simulations of the EW undular bore

Abstract

The equal width equation is solved by a Petrov–Galerkin method using quadratic B-spline spatial finite elements. A linear recurrence relationship for the numerical solution of the resulting system of ordinary differential equations is obtained via a Crank–Nicolson approach involving a product approximation. The motion of solitary waves is studied to assess the properties of the algorithm. The development of an EW undular bore is investigated and compared with that of the RLW bore. © 1997 John Wiley & Sons, Ltd.