The alternating group explicit (AGE) iterative method for variable coefficient parabolic equations

In this paper the alternating group explicit (AGE) iterative method is extended to solve the general linear variable coefficient parabolic equation in one dimension under suitable initial and boundary conditions after an appropriate transformation of the differential equation. The stability of the finite difference equations and the convergence of the AGE method is studied. The AGE methods are tested on the convection-diffusion equations in cartesian, cylindrical and spherical co-ordinates, and the results of the numerical experiments compared. The methods are explicit, accurate and flexible.