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

Abstract

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

Keywords

• Cubic B-splines
• finite element method
• Galerkin
• MRLW equation
• solitary waves.