Approximate Solutions of the Lane-Emden Equations by LS-SVM Method

In this study, approximate solutions of the Lane-Emden differential equation, which plays an importantrole in the literature, were obtained using the Least Squares Support Vector Machines (LS-SVM) method for both linear and nonlinear cases. The Collocation method was employed to define the constraints in the solution process. The system of equations obtained in the linear case was solved directly to determine the unknown parameters, while the Newton-Raphson method was used to solve the nonlinear equation system. The approximate solutions obtained in the applications considered in this study were compared with the exact solution for the linear case; with the analytical solution for the nonlinear case; and with the Adomian Decomposition Method (ADM) in the final application where no analytical solution exists. The results show that the numerical solutions obtained using the LS-SVM method are highly accurate and consistent with the reference results.