Numerical solutions of the MRLW equation by cubic B-spline Galerkin finite element method

In this paper, a numerical solution of the modified regularized long wave (MRLW) equation has been obtained by a numerical technique based on a lumped Galerkin method using cubic B-spline finite elements. Solitary wave motion, interaction of two and three solitary waves have been studied to validate the proposed method. The three invariants ( 1 2 3 I ,I ,I ) of the motion have been calculated to determine the conservation properties of the scheme. Error norms L2 and L∞ have been used to measure the differences between the exact and numerical solutions. Also, a linear stability analysis of the scheme is proposed