A New Tau Method for Solving Nonlinear Lane-Emden Type Equations via Bernoulli Operational Matrix of Differentiation. (20th May 2013)

• Record Type: Journal Article
• Authors: Tohidi, E.; Erfani, Kh.; Gachpazan, M.; Shateyi, S.
• Other Names: Sezer Mehmet Academic Editor.
• Is Part Of: Journal of applied mathematics. Volume 2013(2013)
• Publication Date: 2013-05-20
• Subjects: Mathematics -- Periodicals; 519.05
• DOI: 10.1155/2013/850170
• Languages: English
• ISSNs: 1110-757X

Abstract

Abstract : 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.