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Research Papers

A New Bernoulli Wavelet Operational Matrix of Derivative Method for the Solution of Nonlinear Singular Lane–Emden Type Equations Arising in Astrophysics

[+] Author and Article Information
S. Balaji

Department of Mathematics,
Sastra University,
Thanjavur 613 401, India
e-mail: balaji_maths@yahoo.com

Contributed by the Design Engineering Division of ASME for publication in the JOURNAL OF COMPUTATIONAL AND NONLINEAR DYNAMICS. Manuscript received June 24, 2015; final manuscript received December 28, 2015; published online February 5, 2016. Assoc. Editor: Sotirios Natsiavas.

J. Comput. Nonlinear Dynam 11(5), 051013 (Feb 05, 2016) (11 pages) Paper No: CND-15-1181; doi: 10.1115/1.4032386 History: Received June 24, 2015; Revised December 28, 2015

In this paper, a new method is presented for solving generalized nonlinear singular Lane–Emden type equations arising in the field of astrophysics, by introducing Bernoulli wavelet operational matrix of derivative (BWOMD). Bernoulli wavelet expansions together with this operational matrix method, by taking suitable collocation points, converts the given Lane–Emden type equations into a system of algebraic equations. Solution to the problem is identified by solving this system of equations. Further applicability and simplicity of the proposed method has been demonstrated by some examples and comparison with other recent methods. The obtained results guarantee that the proposed BWOMD method provides the good approximate solution to the generalized nonlinear singular Lane–Emden type equations.

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Figures

Grahic Jump Location
Fig. 1

The BWOMD solution for Example 4.1.1

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Fig. 2

The exact and BWOMD solution for Example 4.1.2

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Fig. 3

The exact and BWOMD solution for Example 4.1.3

Grahic Jump Location
Fig. 4

The exact and BWOMD solution for Example 4.1.4

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Fig. 5

The exact and BWOMD solution for Example 4.1.5

Grahic Jump Location
Fig. 6

The exact and BWOMD solution for Example 4.1.6

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Fig. 7

The exact and BWOMD solution for Example 4.1.7

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Fig. 8

The exact and BWOMD solution for Example 4.2.1

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Fig. 9

The exact and BWOMD solution for Example 4.2.2

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