AN EFFECTIVE NUMERICAL ALGORITHM FOR SOLVING THE LANE-EMDEN TYPE EQUATION BASED ON THE VARIATIONAL ITERATION METHOD COUPLED WITH THE HOMOTOPY ANALYSIS METHOD

This research introduces an effective numerical algorithm to determine the numerical solution of the Lane-Emden equation. This method is based on the variational iteration method coupled with the homotopy analysis method. We also included the convergence study of the proposed algorithm. Eight application problems of the Lane-Emden type equation of various kinds with several types of initial and boundary conditions are included to demonstrate the efficacy and accuracy of the proposed algorithm. The numerical outcomes are contrasted with those obtained by other methods [<span class="xref"><a href="#b12" ref-type="bibr">12</a></span>,<span class="xref"><a href="#b20" ref-type="bibr">20</a></span>,<span class="xref"><a href="#b21" ref-type="bibr">21</a></span>] and the exact solution. Unlike other methods, the proposed algorithm does not require discretization or perturbation and can be applied easily and accurately. The proposed method can solve complex problems with less computational work and computation time.