Numerical Solution of Singular Lane-Emden Type Equations using Clique Polynomial

In this paper, the clique polynomial method (CPM) is proposed for the numerical solution of Singular Lane-Emden type equations. A new operational matrix of integration concerning clique polynomials of the complete graph has been generated in its generalized representation. This operational matrix is applied to differential equations and is transformed into a system of algebraic equations that can be solved efficiently with the help of Newton’s iterative solver. The efficiency of the developed method is revealed by considering illustrative examples, and the obtained results are compared favorably with the corresponding exact solution and errors.