A Petrov–Galerkin method for solving the generalized regularized long wave (GRLW) equation

The generalized regularized long wave (GRLW) equation is solved numerically by the Petrov–Galerkin method which uses a linear hat function as the trial function and a quintic BB-spline function as the test function. Product approximation has been used in this method. A linear stability analysis of the scheme shows it to be conditionally stable. Test problems including the single soliton and the interaction of solitons are used to validate the suggested method, which is found to be accurate and efficient. Finally, the Maxwellian initial condition pulse is studied.