Numerical solutions of RLW equation using Galerkin method with extrapolation techniques

In this paper, we present a new Galerkin method for the regularized long wave (RLW) equation. Based on the Galerkin method using linear finite elements, the extrapolation technique is proposed to increase the order of the time discretization accuracy to O(( ^Δt)2), giving O(( ^Δt)2+ ^h2) overall, which is quite efficient to solve the one-dimensional RLW. A stability analysis based on Von Neumann theory is performed. Propagation of solitary waves, interaction of two solitary waves and undular bores are simulated using the proposed method to validate the method which is found to be accurate and efficient.