A Jacobi–Gauss collocation method for solving nonlinear Lane–Emden type equations

In this paper, a shifted Jacobi–Gauss collocation spectral method is proposed for solving the nonlinear Lane–Emden type equation. The spatial approximation is based on shifted Jacobi polynomials PT,n(α,β)(x) with α, β ∈ (−1, ∞), T > 0, and n is the polynomial degree. The shifted Jacobi–Gauss points are used as collocation nodes. Numerical examples are included to demonstrate the validity and applicability of the technique and a comparison is made with existing results. The method is easy to implement and yields very accurate results.

► A new numerical scheme based on general Jacobi–Gauss collocation method is introduced for Lane–Emden type equation. ► The Jacobi–Gauss collocation method has been easily implemented and gives very accurate results. ► The Lane–Emden type equation using Jacobi–Gauss collocation method is reduced to nonlinear algebraic equations. ► Magnificent numerical results are obtained by selecting few collocation points.