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The optimal modified variational iteration method for the Lane-Emden equations with Neumann and Robin boundary conditions

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Abstract.

An effective analytical technique is proposed for the solution of the Lane-Emden equations. The proposed technique is based on the variational iteration method (VIM) and the convergence control parameter h . In order to avoid solving a sequence of nonlinear algebraic or complicated integrals for the derivation of unknown constant, the boundary conditions are used before designing the recursive scheme for solution. The series solutions are found which converges rapidly to the exact solution. Convergence analysis and error bounds are discussed. Accuracy, applicability of the method is examined by solving three singular problems: i) nonlinear Poisson-Boltzmann equation, ii) distribution of heat sources in the human head, iii) second-kind Lane-Emden equation.

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Authors and Affiliations

  1. Department of Mathematics, Birla Institute of Technology Mesra, 835315, Ranchi, India

    Randhir Singh

  2. Department of Mathematics, Indian Institute of Technology Kharagpur, 721302, Kharagpur, India

    Nilima Das & Jitendra Kumar

Authors
  1. Randhir Singh
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  2. Nilima Das
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  3. Jitendra Kumar
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Correspondence to Randhir Singh.

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Singh, R., Das, N. & Kumar, J. The optimal modified variational iteration method for the Lane-Emden equations with Neumann and Robin boundary conditions. Eur. Phys. J. Plus 132, 251 (2017). https://doi.org/10.1140/epjp/i2017-11521-x

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  • DOI: https://doi.org/10.1140/epjp/i2017-11521-x

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