A study on homotopy analysis method and clique polynomial method

This paper generated the novel approach called the Clique polynomial method (CPM) using the clique polynomials raised in graph theory. Nonlinear initial value problems are converted into nonlinear algebraic equations by discretion with suitable grid points in the current approach. We solved highly nonlinear initial value problems using the Homotopy analysis method (HAM) and Clique polynomial method (CPM). Obtained results reveal that the present technique is better than HAM that is discussed through tables and simulations. Convergence analysis is reflected in terms of theorems.