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Collocation method using cubic B-spline for the generalised equal width equation

The generalised equal width wave (GEW) equation ut + eupux - δuxxt = 0 is solved numerically by a B-spline finite element method. The approach used, is based on collocation of cubic B-splines over finite elements so that we have continuity of the dependent variable and its first two derivatives throughout the solution range. In this research, the scheme of the equation under investigation is found to be unconditionally 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. The three invariants of the motion are evaluated to determine the conservation properties of the generated scheme. Finally, the Maxwellian initial condition pulse is studied.