Solitary waves solutions of the MRLW equation using quintic B-splines

In this paper, B-spline finite element method is used to solve the Modified Regularized Long Wave (MRLW) equation. The proposed approach involves a collocation method using quintic B-splines at the knot points as element shape. Time integration of the resulting system of ordinary differential equation is effected using the fourth order Runge–Kutta method, instead of the difference method. The resulting system of ordinary differential equations is integrated with respect to time. Three invariants of motion are evaluated to determine the conservation properties of the suggested scheme. The suggested numerical scheme leads to accurate and efficient results. Moreover, interaction two and three solitary waves are studied through computer simulation and the development of the Maxwellian initial condition into solitary waves is also shown.