Differential Quadrature Solution of Lane–Emden Equations Using Newton Linearization

This paper presents a numerical method combining the Differential Quadrature Method (DQM) with Newton linearization (DQNL) for solving nonlinear Lane–Emden equations. DQM discretizes the domain, yielding a nonlinear algebraic system solved via Newton’s method. The proposed approach is applied to several test problems with various nonlinearities. Stability under noise perturbations, execution time, and accuracy are thoroughly analyzed. Numerical results show that DQNL achieves high accuracy with few discretization points and iterations, outperforming existing methods in both precision and efficiency.