THE ALTERNATING GROUP EXPLICIT (AGE) ITERATIVE METHOD TO SOLVE PARABOLIC AND HYPERBOLIC PARTIAL DIFFERENTIAL EQUATIONS
Mohd Salleh Sahimi, David John Evans · Annual Reviews of Heat Transfer · 1989
Abstract. In this paper, the alternating group explicit (AGE) iterative method is applied to a nonlinear 4th order PDE describing the flow of an incompressible fluid. This equation is of a Ladyzhenskaya-type. The AGE 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 approximate efficiently solutions to the Navier-Stokes equations and the Ladyzhenskaya equations. Problem 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.