Numerical Treatment for the Coupled-BBM System

Abstract

// In the present paper, a numerical method is proposed for the numerical solution of a coupled-BBM system with appropriate initial and boundary conditions by using collocation method with quintic B-spline on the uniform mesh points. The method is shown to be unconditionally stable using von-Neumann technique. To test accuracy the error norms \(L_2\), \(L_\infity\) are computed. Furthermore, interaction of two and three solitary waves are used to discuss the effect of the behavior of the solitary waves after the interaction. These results show that the technique introduced here is easy to apply. We make linearization for the nonlinear term.