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

## Keywords:

Cubic B-splines, finite element method, Galerkin, MRLW equation, solitary waves.## 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.## References

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