An Efficient Approach to Numerical Study of the MRLW Equation with B-Spline Collocation Method

Abstract

A septic B-spline collocation method is implemented to find the numerical solution of the modified regularized long wave (MRLW) equation. Three test problems including the single soliton and interaction of two and three solitons are studied to validate the proposed method by calculating the error norms $L_2$ and $L_{\mathrm{\infty }}$ and the invariants $I_1$, $I_2$, and $I_3$. Also, we have studied the Maxwellian initial condition pulse. The numerical results obtained by the method show that the present method is accurate and efficient. Results are compared with some earlier results given in the literature. A linear stability analysis of the method is also investigated.