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 presented method is based on the Tau method together with the Bernoulli polynomial approximations in which a new o...

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Bibliographic Details
Published in:Journal of Applied Mathematics 2013-01, Vol.2013 (2013), p.561-569-757
Main Authors: Tohidi, Emran, Erfani, Kh, Gachpazan, M., Shateyi, Stanford
Format: Article
Language:English
Subjects:
Approximation theory
Astrophysics
Differential equations, Nonlinear
Mathematical physics
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Summary: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.
ISSN:1110-757X
1687-0042
DOI:10.1155/2013/850170