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

作者：Bhrawy A H^*; Alofi A S

来源：Communications in Nonlinear Science & Numerical Simulation, 2012, 17(1): 62-70.

DOI：10.1016/j.cnsns.2011.04.025

• Lane-Emden type equation
• Second-order initial value problems
• Collocation method
• Jacobi-Gauss quadrature
• Shifted Jacobi polynomials

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 P(T,beta)((x,beta)) (x) with alpha, beta is an element of (-1, infinity), 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.

• 出版日期2012-1