Hybrid Functions for Nonlinear Differential Equations with Applications to Physical Problems

摘要

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 functions of block-pulse functions and Bernoulli polynomials are presented and are utilized to reduce the computation of nonlinear initial-value problems to a system of equations. The method is easy to implement and yields very accurate results.