Title: Approximate solutions of linear and non-linear diffusion equations by using Daftardar-Gejji-Jafari's method
Authors: Murat Sari; Abdurrahim Gunay; Gurhan Gurarslan
Addresses: Department of Mathematics, Faculty of Art and Science, Pamukkale University, Denizli 20070, Turkey. ' Department of Mathematics, Faculty of Art and Science, Pamukkale University, Denizli 20070, Turkey. ' Department of Civil Engineering, Faculty of Engineering, Pamukkale University, Denizli 20070, Turkey
Abstract: This study discovers the utility of the Daftardar-Gejji-Jafari|s (DGJ) method to obtain approximate solution of the linear and non-linear diffusion equations. The method gives reliable results in the form of analytical approximation. Thus, the method is seen to be a very reliable alternative tool for finding analytical solutions of more complex equations. Use of small parameter or linearisation is not needed in the present approach as opposed to numerical methods. The aim of this work is to derive approximations to the solution of the diffusion equations. The method and its ability are illustrated in solving seven examples. The obtained solutions converge to the analytical solutions and are in very good agreement with the literature. The proposed method is realised to be more cost-effective in terms of computation. The DGJ method is seen to be a very good alternative to existing iterative techniques.
Keywords: linear diffusion equations; nonlinear diffusion equations; ODE; PDE; new iterative method; iterative series methods.
International Journal of Mathematical Modelling and Numerical Optimisation, 2011 Vol.2 No.4, pp.376 - 386
Received: 02 Feb 2010
Accepted: 08 Sep 2010
Published online: 14 Oct 2011 *