An efficient computational approach to solving singular initial value problems for Lane–Emden type equations

• Zdeněk Šmarda ^[1] ; Yasir Khan ^[2]
  1. [1] Brno University of Technology

     Brno University of Technology

     Chequia

     
  2. [2] University of Hafr Al-Batin

     University of Hafr Al-Batin

     Arabia Saudí

     
• Localización: Journal of computational and applied mathematics, ISSN 0377-0427, Vol. 290, Nº 1, 2015, págs. 65-73
• Idioma: inglés
• DOI: 10.1016/j.cam.2015.04.045
• Enlaces
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• Resumen

  • In the paper, we present the new computational approach for solving singular initial problems for the Lane–Emden type equations with nonlinear terms based on the differential transformation method (DTM) and the modified general formula for the Adomian polynomials with differential transformation components. To illustrate the capability and efficiency of the method three examples are given. The results obtained in this work are also compared with numerical results of Heydari et al. (2012), Wazwaz (2005), Singh et al. (2009) and the standard DTM as well. These results show that the proposed technique, without linearization or small perturbation, is very effective and convenient for solving of linear and nonlinear differential equations.