In this paper, we present numerical solutions for the Lane-Emden equation using the double exponential non-classical sinc collocation method for polytropic indices \(r = 1, 2, 3, 4\) , and \(5\) . The singular behavior of the Lane-Emden equation poses a significant challenge, which we address by augmenting the traditional sinc expansion with weight functions—a key innovation of our approach. We utilized the properties of this method, we transform the nonlinear problem into a system of algebraic equations. The implementation is both straightforward and computationally efficient. We present results for three different weight functions for each polytropic index: \(w(x)=1\) , \(w(x)=x\) , and \(w(x)=sin(x)\) . Finally, we compare our results with those documented in the literature by applying our method to two of their examples. This comparison highlights the superior performance of our method over existing approaches.
