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Solutions of Emden-Fowler type Equations by Variational Iteration Method

Yıl 2019, Cilt: 16 Sayı: 2, 1 - 9, 01.11.2019

Öz

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


Kaynakça

  • [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.
Yıl 2019, Cilt: 16 Sayı: 2, 1 - 9, 01.11.2019

Öz

Kaynakça

  • [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.
Toplam 16 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Mühendislik
Bölüm Makaleler
Yazarlar

Morufu Oyedunsi Olayıwola

Yayımlanma Tarihi 1 Kasım 2019
Yayımlandığı Sayı Yıl 2019 Cilt: 16 Sayı: 2

Kaynak Göster

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. Kasım 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, sy. 2 (Kasım 2019): 1-9.
EndNote Olayıwola MO (01 Kasım 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, c. 16, sy. 2, ss. 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 (Kasım 2019), 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, c. 16, sy. 2, 2019, ss. 1-9.
Vancouver Olayıwola MO. Solutions of Emden-Fowler type Equations by Variational Iteration Method. CUJSE. 2019;16(2):1-9.