Hybrid functions for nonlinear initial-value problems with applications to Lane–Emden type equations

A numerical method for solving nonlinear initial-value problems is proposed. The Lane–Emden type equations which have many applications in mathematical physics are then considered. The method is based upon hybrid function approximations. The properties of hybrid of block-pulse functions and Lagrange interpolating polynomials are presented and are utilized to reduce the computation of nonlinear initial-value problems to a system of non-algebraic equations. The method is easy to implement and yields very accurate results.