SOLUTION OF LANE-EMDEN TYPE EQUATIONS ARISING IN ASTROPHYSICS BASED ON A HYBRID DISCRETIZATION SCHEME

In this paper, a composite Chebyshev nite di erence method for solving nonlinear initial-value problems is successfully implemented. The Lane -Emden type equations which have many applications in mathematical physics and astrophysics are then investigated. They are categorized as singular initial-value problems. The proposed approximation method is based on a hybrid of blockpulse functions and Chebyshev polynomials. Our approach is an extension of Chebyshev nite difference scheme. The nice properties of hybrid functions together with the well-known Chebyshev Gauss-Lobatto points are then used to transform the main problem into a system of nonlinear algebraic equations whose solution is much easier than the original one. The convergence of the method is discussed. Several numerical experiments are examined to show the e ectiveness of the suggested discretization scheme.