An Effective Numerical Approach Based on Collocation Method for the Generalized Rosenau-RLW-Burgers Equation

This article related with the numerical solutions of the generalized Rosenau-RLW- Burgers (G-RRB) equation procured by coupling Rosenau-RLW equation and Rosenau–Burgers equation. To reach this goal, collocation method and septic B-spline basis functions have been employed as a polynomial approximation to the solution. It is proved by applying von-Neumann stability analysis that the numerical method is unconditionally stable. A test problem is successfully solved by calculating \(L_{2}\) and \(L_{\infty }\) error norms for illustrate the adequacy and efficiency of the method. It is made an inference that the numerical results match well with the analytical solutions, which indicates that the current B-spline collocation algorithm is an attractive and powerful algorithm. The obtained results have been presented both in tables and graphically. As can be seen from the tables and graphs that the suggested method is quantitively interesting, influential, confidential, and powerful for solving several physical models in science and engineering.