In this work, a numerical solution of the modified regularized long wave (MRLW)
equation is obtained by the method based on collocation of quintic B-splines over
the finite elements. A linear stability analysis shows that the numerical scheme based
on Von Neumann approximation theory is unconditionally stable. Test problems
including the solitary wave motion, the interaction of two and three solitary waves
and the Maxwellian initial condition are solved to validate the proposed method by
calculating error norms L2 and L∞ that are found to be marginally accurate and
efficient. The three invariants of the motion have been calculated to determine the
conservation properties of the scheme. The obtained results are compared with other
earlier result
