Solitary Pattern Solutions of gBBM Equation using New Iterative Method (NIM)

Abstract

In this study, we focus on the solitary pattern solutions of the generalized Benjamin-Bona-Mahony equations (gBBM) and propose a new iterative method (NIM) for their numerical solution, given suitable initial conditions. Our proposed NIM approach generates numerical solutions in the form of a convergent power series with computationally simple components. Our results demonstrate that the NIM approach exhibits exceptional performance in terms of accuracy, efficiency, simplicity, stability, and reliability.