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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.
Highlights
This equation is investigated using a semi-analytical method called the Variation of parameters method with an auxiliary parameter
An unknown auxiliary parameter is inserted in Variation of Parameters Method to solve some special cases of these equations
Singh et al [13] suggested an effective analytic algorithm using Modified Homotopy Analysis Method (MHAM), at which convergence regions could be adjusted without using Pade’s technique. Another algorithm was proposed in [14], using an iterative method which is a hybrid of Adomian’s Decomposition Method (ADM) and Variational Iteration Method (VIM)
Summary
Singh et al [13] suggested an effective analytic algorithm using Modified Homotopy Analysis Method (MHAM), at which convergence regions could be adjusted without using Pade’s technique. Another algorithm was proposed in [14], using an iterative method which is a hybrid of ADM and Variational Iteration Method (VIM).
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