International Journal of Computer Mathematics Vol. 85, No. 2, February 2008, 287–305 The alternating group explicit (AGE) iterative method for solving a Ladyzhenskaya model for stationary incompressible viscous flow F. FAIRAG*† and M. S. SAHIMI§‡ †Department of Mathematics and Statistics, King Fahd University of Petroleum & Minerals, Dhahran, 31261 Saudi Arabia ‡Department of Engineering Sciences and Mathematics, Universiti Tenaga Nasional, 43009 Kajang, Selangor, Malaysia (Received 24 August 2005; revised version received 23 March 2007; accepted 24 April 2007) In this paper, the alternating group explicit (AGE) iterative method is applied to a nonlinear fourth- order PDE describing the flow of an incompressible fluid. This equation is a Ladyzhenskaya equation. TheAGE method is shown to be extremely powerful and flexible and affords its users many advantages. Computational results are obtained to demonstrate the applicability of the method on some problems with known solutions. This paper demonstrates that the AGE method can be implemented to approxi- mate solutions efficiently to the Navier–Stokes equations and the Ladyzhenskaya equations. Problems with a known solution are considered to test the method and to compare the computed results with the exact values. Streamfunction contours and some plots are displayed showing the main features of the solution. Keywords: Alternating Group Explicit (AGE) method; Ladyzhenskaya equations; Navier–Stokes equations C.R. Category: G.1.8 1. Introduction Understanding turbulent flow is central to many important problems including environmental and energy related applications (global change, mixing of fuel and oxidizer in engines and drag reduction), aerodynamics (maneuvering flight of jet aircraft) and biophysical applications (blood flow in the heart). However, in many situations it is still not clear which models are most appropriate, especially in the case of turbulent flows. The Navier–Stokes equations are generally accepted as providing an accurate model for the incompressible motion of viscous fluids in practical situations. This research will consider one model introduced by Ladyzhenskaya [1–3]. The study of this model may be justified *Corresponding author. Email: ffairag@kfupm.edu.sa §Email: sallehs@uniten.edu.my International Journal of Computer Mathematics ISSN 0020-7160 print/ISSN 1029-0265 online © 2008 Taylor & Francis http://www.tandf.co.uk/journals DOI: 10.1080/00207160701455894