The research paper deals with the numerical solutions of the Rosenau- Hymann (R-H) equation, known as the generalized Korteweg-de Vries equation, which represents the dynamics of shallow water waves and models of pattern formation in liquid drops. To reach this aim based on septic B-spline approximation, a collocation finite element method has been offered and applied for numerical solutions of R-H equation conceiving different parameter values of test problem. Also, Von-Neumann stability analysis has been performed which guarantees that the scheme is unconditionally stable. A test problem has been successfully solved by calculating L 2 and L ∞ error norms for illustrate the proficiency and reliability of the method and highlighted the significance of this work. 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. Also to reflect the efficiency of this method for solving the nonlinear equation, the results are depicted both graphically and in tabular form. The results obtained from both analytical and numerical methods show us that this study will be very useful for scientists concern with searching characteristics features of nonlinear phenomena in several fields of science.