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A Representation of the Exact Solution of Generalized Lane‐Emden Equations Using a New Analytical Method

Author

Listed:
  • Omar Abu Arqub
  • Ahmad El-Ajou
  • A. Sami Bataineh
  • I. Hashim

Abstract

A new analytic method is applied to singular initial‐value Lane‐Emden‐type problems, and the effectiveness and performance of the method is studied. The proposed method obtains a Taylor expansion of the solution, and when the solution is polynomial, our method reproduces the exact solution. It is observed that the method is easy to implement, valuable for handling singular phenomena, yields excellent results at a minimum computational cost, and requires less time. Computational results of several test problems are presented to demonstrate the viability and practical usefulness of the method. The results reveal that the method is very effective, straightforward, and simple.

Suggested Citation

  • Omar Abu Arqub & Ahmad El-Ajou & A. Sami Bataineh & I. Hashim, 2013. "A Representation of the Exact Solution of Generalized Lane‐Emden Equations Using a New Analytical Method," Abstract and Applied Analysis, John Wiley & Sons, vol. 2013(1).
    • Handle: RePEc:wly:jnlaaa:v:2013:y:2013:i:1:n:378593
    DOI: 10.1155/2013/378593
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    References listed on IDEAS

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    1. Omar Abu Arqub & Mohammed Al-Smadi & Shaher Momani, 2012. "Application of Reproducing Kernel Method for Solving Nonlinear Fredholm-Volterra Integrodifferential Equations," Abstract and Applied Analysis, Hindawi, vol. 2012, pages 1-16, September.
    2. Omar Abu Arqub & Mohammed Al-Smadi & Shaher Momani, 2012. "Application of Reproducing Kernel Method for Solving Nonlinear Fredholm‐Volterra Integrodifferential Equations," Abstract and Applied Analysis, John Wiley & Sons, vol. 2012(1).
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    Cited by:

    1. Mubashir Qayyum & Qursam Fatima, 2022. "Solutions of Stiff Systems of Ordinary Differential Equations Using Residual Power Series Method," Journal of Mathematics, John Wiley & Sons, vol. 2022(1).
    2. Mubashir Qayyum & Amna Khan, 2022. "Constructing and Predicting Solutions for Different Families of Partial Differential Equations: A Reliable Algorithm," Journal of Mathematics, John Wiley & Sons, vol. 2022(1).

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