Open AccessA New Tau Method for Solving Nonlinear Lane-Emden Type Equations via Bernoulli Operational Matrix of Differentiation
Author(s) -
Emran Tohidi,
Kh. Erfani,
M. Gachpazan,
Stanford Shateyi
Publication year - 2013
Publication title -
journal of applied mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.307
H-Index - 43
eISSN - 1687-0042
pISSN - 1110-757X
DOI - 10.1155/2013/850170
Subject(s) - bernoulli's principle , nonlinear system , maple , matrix (chemical analysis) , type (biology) , mathematics , algebraic equation , polynomial , scheme (mathematics) , bernoulli polynomials , algebraic number , computer science , mathematical optimization , mathematical analysis , classical orthogonal polynomials , ecology , physics , botany , materials science , quantum mechanics , composite material , orthogonal polynomials , biology , engineering , aerospace engineering
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 presented method is based on the Tau method together with the Bernoulli 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 several mild conditions the error analysis of the proposed method is provided. Several examples are included to illustrate the efficiency and accuracy of the proposed technique and also the results are compared with the different methods. All calculations are done in Maple 13
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