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Solution of Lane–Emden type equations using rational Bernoulli functions
Author(s) -
Calvert Velinda,
Mashayekhi Somayeh,
Razzaghi Mohsen
Publication year - 2016
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.3570
Subject(s) - mathematics , bernoulli's principle , bernoulli differential equation , type (biology) , nonlinear system , ordinary differential equation , algebraic equation , rational function , derivative (finance) , product (mathematics) , domain (mathematical analysis) , algebraic number , mathematical analysis , differential algebraic equation , differential equation , geometry , ecology , physics , quantum mechanics , aerospace engineering , financial economics , engineering , economics , biology
In this paper, a numerical method for solving Lane‐Emden type equations, which are nonlinear ordinary differential equations on the semi‐infinite domain, is presented. The method is based upon the modified rational Bernoulli functions; these functions are first introduced. Operational matrices of derivative and product of modified rational Bernoulli functions are then given and are utilized to reduce the solution of the Lane‐Emden type equations to a system of algebraic equations. Illustrative examples are included to demonstrate the validity and applicability of the technique. Copyright © 2015 John Wiley & Sons, Ltd.