A B‐spline finite element method for the regularized long wave equation

Abstract

Abstract A B‐spline finite element method is used to solve the regularized long wave equation numerically. This approach involves a Galerkin method with quadratic B‐spline finite elements so that there is continuity of the dependent variable and its first derivative throughout the solution range. Time integration of the resulting system of ordinary differential equations is effected using a Crank‐Nicolson approximation. Standard problems are used to validate the algorithm, which is then used to model the smooth development of an undular bore.