A New Tau Method for Solving Nonlinear Lane-Emden Type Equations via Bernoulli Operational Matrix of Differentiation

A new and efficient numerical approach is developed for solving nonlinear Lane-Emden type equations via Bernoulli operational matrix of differentiation.The fundamental structure of the presentedmethod is based on theTaumethod togetherwith theBernoulli polynomial approximations in which a new operational matrix is introduced. After implementation of our scheme, the main problem would be transformed into a system of algebraic equations such that its solutions are the unknown Bernoulli coefficients. Also, under severalmild conditions the error analysis of the proposedmethod is provided. Several examples are included to illustrate the efficiency and accuracy of the proposed technique and also the results are compared with the differentmethods. All calculations are done in Maple 13.