Approximate Solution of Lane-Emden Type Equations Using Variation of Parameters Method with an Auxiliary Parameter - Journal of Applied Mathematics and Physics

JAMP > Vol.7 No.4, April 2019

Approximate Solution of Lane-Emden Type Equations Using Variation of Parameters Method with an Auxiliary Parameter ()

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DOI: 10.4236/jamp.2019.74062 1,238 Downloads 3,580 Views Citations

Author(s)

Asmaa S. Khalifa, Hany N. Hassan^*

Affiliation(s)

Department of Basic Engineering Sciences, Benha Faculty of Engineering, Benha University, Benha, Egypt.

ABSTRACT

Lane-Emden type equation is a nonlinear differential equation appears in many fields such as stellar structure, radioactive cooling and modeling of clusters of galaxies. In this work, this equation is investigated using a semi-analytical method called the Variation of parameters method with an auxiliary parameter. In the applied technique, an unknown auxiliary parameter is inserted in Variation of Parameters Method to solve some special cases of these equations. The used algorithm is easy to implement and very effective. The obtained solutions are also fairly accurate.

KEYWORDS

Lane-Emden Equation, Variation of Parameter Method (VPM), Auxiliary Parameter

Share and Cite:

Khalifa, A. and Hassan, H. (2019) Approximate Solution of Lane-Emden Type Equations Using Variation of Parameters Method with an Auxiliary Parameter. Journal of Applied Mathematics and Physics, 7, 921-941. doi: 10.4236/jamp.2019.74062.

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