M. M. Rashidi and M. Keimanesh, “Using Differential Transform Method and the Padé Approximant for Solving MHD Flow in a Laminar Liquid Film from a Horizontal Stretching Surface,” Mathematical Problem in Engineering, Vol. 2010, Article ID 491319.

has been cited by the following article:

• TITLE: Application of Multi-Step Differential Transform Method on Flow of a Second-Grade Fluid over a Stretching or Shrinking Sheet

  AUTHORS: M.M Rashidi, Ali J. Chamkha, M Keimanesh

  KEYWORDS: Non-Newtonian Fluid, Stretching Surface, Shrinking Sheet, Multi-Step Differential Transform Method (MDTM)

  JOURNAL NAME: American Journal of Computational Mathematics, Vol.1 No.2, July 4, 2011

  ABSTRACT: In this study, a reliable algorithm to develop approximate solutions for the problem of fluid flow over a stretching or shrinking sheet is proposed. It is depicted that the differential transform method (DTM) solutions are only valid for small values of the independent variable. The DTM solutions diverge for some differential equations that extremely have nonlinear behaviors or have boundary-conditions at infinity. For this reason the governing boundary-layer equations are solved by the Multi-step Differential Transform Method (MDTM). The main advantage of this method is that it can be applied directly to nonlinear differential equations without requiring linearization, discretization, or perturbation. It is a semi analytical-numerical technique that formulizes Taylor series in a very different manner. By applying the MDTM the interval of convergence for the series solution is increased. The MDTM is treated as an algorithm in a sequence of intervals for finding accurate approximate solutions for systems of differential equations. It is predicted that the MDTM can be applied to a wide range of engineering applications.