In this paper, a numerical technique for solving the regularised long wave equation (RLW) is presented using a wavelet Galerkin (WG) method in space and a fourth-order Runge–Kutta (RK) technique in time.We study the convergence analysis of the obtained numerical solutions and investigate the results for the motions of double and single solitary waves, undular bores and conservation properties of mass, energy and momentum in order to verify the applicability and performance of the proposed method. Simulation results are further compared with the known analytical solutions and some previous published numerical results. It is concluded that the present method remarkably improves the accuracy of the Galerkin-based methods for numerically solving a large class of nonlinear and weakly dispersive ocean waves.
