Solutions of Emden-Fowler type Equations by Variational Iteration Method
Year 2019,
Volume: 16 Issue: 2, 1 - 9, 01.11.2019
Morufu Oyedunsi Olayıwola
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
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Year 2019,
Volume: 16 Issue: 2, 1 - 9, 01.11.2019
Morufu Oyedunsi Olayıwola
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.