An efficient numerical method supports the numerical solution of nonlinear wave equations. This method is characterized by the regularized long wave equations (RLWs) along with their generalization (GRLW). The newly redesigned method uses a pseudo-spectral treatment (Fourier transform) of the space dependence along an implicit pattern timely linearized. A significant advantage of employing this method, is the ability to vary the length of the mesh, reducing computation times. Using linear stability analysis, uou can see that the suggested method is unconditionally constant. It is quadratic in time and is the general order of space. The described method is related to the RLW equation and its generalized shape. However, it may be performed in a large category of nonlinear long-wave equations (2),There are clear changes in the different expressions. Test questions including some simulations of solitons and solitary wave interactions. These are employed to test methods that have been found to be accurate and effective. Three kinetic constants are assessed to detect the conservation characteristics of the algorithm
