Numerical-Solution-For-Nonlinear-Klein–Gordon Equation via Operational-Matrix by Clique Polynomial of Complete Graphs

Abstract

This study introduced a generalized operational matrix using Clique polynomials of a complete graph and proposed the latest approach to solve the non-linear Klein–Gordon (KG) equation. KG equations describe many real physical phenomena in fluid dynamics, electrical engineering, biogenetics, tribology. By using the properties of the operational-matrix, we transform-the non-linear KG equation into a system-of algebraic-equations. Unknown coefficients to be determined by Newton's method. The present-technique is applied-to four problems, and the obtained-results are-compared with-another-method in the literature. Also, we discussed some theorems on convergence analysis and continuous property