Maryam Jalili - Department of Mathematics, Neyshabur Branch, Islamic Azad University, Neyshabur, Iran

This study is investigated an efficient numerical technique called Clique polynomial method (CPM) usingthe Clique polynomials of the Complete graph. Utilizing discretization with suitable grid points, nonlinearinitial value problems are converted into nonlinear algebraic equations. The present technique is applied toseveral problems, and the obtained results are compared with other methods in the existing literature such asHomotopy analysis method (HAM) and Adomian decomposition method (ADM) through simulations, andtables. Also, we discussed some theorems on convergence analysis and continuous properties.

Clique polynomial method, Nonlinear Differential equation, Complete graph, Convergenceanalysis, Homotopy analysis method (HAM), Adomian decomposition method (ADM).