Comparative study of Adomian decomposition 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 discretization with suitable grid points in the current approach. We solved highly nonlinear initial value problems using the Adomian decomposition method (ADM) and CPM. Obtained results reveal that the present technique is better than ADM that is discussed through tables and simulations.