Collocation method using cubic spline for the rlw equation

摘要

A Collocation method is presented here for the Regularized Long Wave (RLW) equation by using Cubic B-spline as element shape functions. A linear stability analysis showed the scheme to be unconditionally stable. Test problems, including the migration and interaction of solitary waves, are used to validate the method, which found to be accurate and efficient. The three invariants of the motion are evaluated to determine the conservation properties of the algorithm. The temporal evaluation of a Maxwellian initial pulse is then studied, and then we prove that the number of solitons which are generated from Maxwellian initial condition are determined and we compare our results with earlier studies.