A rapid numerical method for nonlinear generalized time-fractional kawahara equations via domination polynomials of complete graph

Abstract

The key objective of this study is to examine the nonlinear Time-fractional generalized Kawahara equation (N-TF-GKE), a significant nonlinear equation that appears in a variety of physical domains, including ion-acoustic waves in plasmas, shallow water waves, and nonlinear acoustics. This Equation exhibits complex dynamic properties, most notably the appearance of shock waves, solitary waves, and chaotic solutions. We use a graph theoretic polynomial approach to obtain numerical solutions of the N-TF-GKE. We present the dominance polynomials of complete graphs (DPC), a new class of graph polynomials, to develop an efficient operational integration matrix to approximate the N-TF-GKE. The N-TF-GKE transformed into a collection of nonlinear algebraic equations with the standard collocation points. We acquire the numerical solutions for the Domination polynomial using Newton's approach. We validate the efficiency and robustness of our domination polynomial collocation method (DCM) with a set of numerical experiments and comparative analyses.