More Efficient Solutions for Numerical Analysis of the Nonlinear Generalized Regularized Long Wave (Grlw) Using the Operator Splitting Method

Through the use of two numerical techniques, the purpose of this study is to examine the approximate outcomes of the (GRLW) equation. The utilized methods are the collocation method with quintic B-spline, which is based on finite elements and yields good results for nonlinear evolution equations, and the strang splitting technique, which is simple to apply, practical, and quick. In order to provide approximate solutions for the main problem, the collocation method is combined with the Strang splitting method for this study. Three examples—the formation of the Maxwellian initial condition, the interaction of two solitary waves, and a single solitary wave—are taken into consideration in order to assess the accuracy of these algorithms. To demonstrate how closely the exact solutions close to numerical results and to contrast them with other solutions in the literature, error norms, and conservation quantities are computed. Tables and graphs are used to illustrate the solutions that have generated. Based on the results obtained and the practical, easy-to-use, and current features of the methodologies, this article stands out from the rest.