Solving the Modified Regularized Long Wave Equations via Higher Degree B-Spline Algorithm

Abstract

The current article considers the sextic B-spline collocation methods (SBCM1 and SBCM2) to approximate the solution of the modified regularized long wave ( $\text{MRLW}$ ) equation. In view of this, we will study the solitary wave motion and interaction of higher (two and three) solitary waves. Also, the modified Maxwellian initial condition into solitary waves is studied. Moreover, the stability analysis of the methods has been discussed, and these will be unconditionally stable. Moreover, we have calculated the numerical conserved laws and error norms ${\mathcal{L}}_2$ and ${\mathcal{L}}_{\infty }$ to demonstrate the efficiency and accuracy of the method. The numerical examples are presented to illustrate the applications of the methods and to compare the computed results with the other methods. The results show that our proposed methods are more accurate than the other methods.