Research Article
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Solutions of Emden-Fowler type Equations by Variational Iteration Method

Year 2019, Volume: 16 Issue: 2, 1 - 9, 01.11.2019

Abstract

In this research article, a numerical approach
to the solutions of different forms of Emden-Fowler is presented. The variational
Iteration Method (VIM) has been applied to a wide class of problems in
mathematical physics, biology and chemical reactions. The solutions provided in
this research proved that the method converged rapidly with easily computable
terms


References

  • [1]. J. H. He, A new approach to nonlinear partial differential equation. Commun. Nonlinear Sci. Numer. Simul. 2(4), (1997), 230-235
  • [2]. J. H. He, Approximate analytical solution for seepage flow with functional derivatives in porous media. Comput. Methods Appl. Mech. Engrg. 167, (1998), 57-68
  • [3]. J. H. He Approximate solution of nonlinear differential equations with convolution roduct non-linearities. Comput. Methods Appl. Mech. Engrg. 167, (1998), 69-73
  • [4]. M. O. Olayiwola. Application of Variational iteration method to linear and nonlinear stiff differential equations. Nigerian Journal of Mathematics and Application 27, (2018), 27-41.
  • [5]. M. O. Olayiwola, P. Ozoh, M. A. Usman and A. W. Gbolagade. On the numerical solution of linear and nonlinear Fredholm integral equations. Nigerian Journal of Mathematics and Application 27, (2018), 68-75.
  • [6]. X. Shang, P. Wu, X. Shao, An efficient method for solving Emden-Fowler equations. J. Franklin Institute 2009, 346, (2009), 889-897.
  • [7]. A. M. Wazwaz, Analytical solution for the time-dependent Emden-Fowler type equation by Adomian decomposition method, Appl, Math. Comput. 166, (2005), 638-651.
  • [8]. A. M. Wazwaz, A new method for solving differential equations of the Lane-Emden type. Appl Math. Comput. 118 (2/3), (2001), 287-310.
  • [9]. A. Aslanov, Approximate solutions of Emden-Fowler type equations. Int. J. Comput. Math. 86(5), (2009), 807-826.
  • [10]. A. Yildirim, T. Ozis, Solutions of singular IVPs of Lane-Emden type by homotopy perturbation method, Phys. Lett. A 2007, 369, (2007), 70-76.
  • [11]. A. M. Wazwaz and Suheil A. Khuri, The Variational Iteration method for solving the Voltera Integro-differential forms of the Lane-Emden and the Emden-Fowler problems with intial value conditions. Open Eng. 5, (2015), 31-41.
  • [12]. O. Kiymaz Variational Iteration Methods for a class of nonlinear differential equations, Int J. Contemp. Math. Sciences, Vol. 5, No. 37, (2010), 1819-1826.
  • [13]. H. Demir, I. C. Sungu, Numerical solution of a class of nonlinear Emden-Fowler equations by using differential transform method. Journal of Arts and Sciences Sayt 12/Arahk 2009, (2009), 75-82.
  • [14]. O. Kiymaz, S. Mirasyedioglu, A new symbolic computational approach to singular initial value problems on the second order ordinary differential equations. Applied Mathematics and Computation 171, (2005), 1218-1225.
  • [15]. R. Chaharpashlou, A parametric iteration method for solving Lane-Emden type equations. Iranian Journal of Numerical Analysis and Optimization, Vol 7, No 1, (2017), 33-45.
  • [16]. H. Aminikhah, S. Moradian, Numerical solution of singular Lane-Emden equation. ISRN Mathematical Physics, Vol 2013, (2013), 1-9.

Year 2019, Volume: 16 Issue: 2, 1 - 9, 01.11.2019

Abstract

References

  • [1]. J. H. He, A new approach to nonlinear partial differential equation. Commun. Nonlinear Sci. Numer. Simul. 2(4), (1997), 230-235
  • [2]. J. H. He, Approximate analytical solution for seepage flow with functional derivatives in porous media. Comput. Methods Appl. Mech. Engrg. 167, (1998), 57-68
  • [3]. J. H. He Approximate solution of nonlinear differential equations with convolution roduct non-linearities. Comput. Methods Appl. Mech. Engrg. 167, (1998), 69-73
  • [4]. M. O. Olayiwola. Application of Variational iteration method to linear and nonlinear stiff differential equations. Nigerian Journal of Mathematics and Application 27, (2018), 27-41.
  • [5]. M. O. Olayiwola, P. Ozoh, M. A. Usman and A. W. Gbolagade. On the numerical solution of linear and nonlinear Fredholm integral equations. Nigerian Journal of Mathematics and Application 27, (2018), 68-75.
  • [6]. X. Shang, P. Wu, X. Shao, An efficient method for solving Emden-Fowler equations. J. Franklin Institute 2009, 346, (2009), 889-897.
  • [7]. A. M. Wazwaz, Analytical solution for the time-dependent Emden-Fowler type equation by Adomian decomposition method, Appl, Math. Comput. 166, (2005), 638-651.
  • [8]. A. M. Wazwaz, A new method for solving differential equations of the Lane-Emden type. Appl Math. Comput. 118 (2/3), (2001), 287-310.
  • [9]. A. Aslanov, Approximate solutions of Emden-Fowler type equations. Int. J. Comput. Math. 86(5), (2009), 807-826.
  • [10]. A. Yildirim, T. Ozis, Solutions of singular IVPs of Lane-Emden type by homotopy perturbation method, Phys. Lett. A 2007, 369, (2007), 70-76.
  • [11]. A. M. Wazwaz and Suheil A. Khuri, The Variational Iteration method for solving the Voltera Integro-differential forms of the Lane-Emden and the Emden-Fowler problems with intial value conditions. Open Eng. 5, (2015), 31-41.
  • [12]. O. Kiymaz Variational Iteration Methods for a class of nonlinear differential equations, Int J. Contemp. Math. Sciences, Vol. 5, No. 37, (2010), 1819-1826.
  • [13]. H. Demir, I. C. Sungu, Numerical solution of a class of nonlinear Emden-Fowler equations by using differential transform method. Journal of Arts and Sciences Sayt 12/Arahk 2009, (2009), 75-82.
  • [14]. O. Kiymaz, S. Mirasyedioglu, A new symbolic computational approach to singular initial value problems on the second order ordinary differential equations. Applied Mathematics and Computation 171, (2005), 1218-1225.
  • [15]. R. Chaharpashlou, A parametric iteration method for solving Lane-Emden type equations. Iranian Journal of Numerical Analysis and Optimization, Vol 7, No 1, (2017), 33-45.
  • [16]. H. Aminikhah, S. Moradian, Numerical solution of singular Lane-Emden equation. ISRN Mathematical Physics, Vol 2013, (2013), 1-9.
There are 16 citations in total.

Details

Primary Language English
Subjects Engineering
Journal Section Research Article
Authors

Morufu Oyedunsi Olayıwola

Publication Date November 1, 2019
Published in Issue Year 2019 Volume: 16 Issue: 2

Cite

APA Olayıwola, M. O. (2019). Solutions of Emden-Fowler type Equations by Variational Iteration Method. Cankaya University Journal of Science and Engineering, 16(2), 1-9.
AMA Olayıwola MO. Solutions of Emden-Fowler type Equations by Variational Iteration Method. CUJSE. November 2019;16(2):1-9.
Chicago Olayıwola, Morufu Oyedunsi. “Solutions of Emden-Fowler Type Equations by Variational Iteration Method”. Cankaya University Journal of Science and Engineering 16, no. 2 (November 2019): 1-9.
EndNote Olayıwola MO (November 1, 2019) Solutions of Emden-Fowler type Equations by Variational Iteration Method. Cankaya University Journal of Science and Engineering 16 2 1–9.
IEEE M. O. Olayıwola, “Solutions of Emden-Fowler type Equations by Variational Iteration Method”, CUJSE, vol. 16, no. 2, pp. 1–9, 2019.
ISNAD Olayıwola, Morufu Oyedunsi. “Solutions of Emden-Fowler Type Equations by Variational Iteration Method”. Cankaya University Journal of Science and Engineering 16/2 (November2019), 1-9.
JAMA Olayıwola MO. Solutions of Emden-Fowler type Equations by Variational Iteration Method. CUJSE. 2019;16:1–9.
MLA Olayıwola, Morufu Oyedunsi. “Solutions of Emden-Fowler Type Equations by Variational Iteration Method”. Cankaya University Journal of Science and Engineering, vol. 16, no. 2, 2019, pp. 1-9.
Vancouver Olayıwola MO. Solutions of Emden-Fowler type Equations by Variational Iteration Method. CUJSE. 2019;16(2):1-9.