The Arithmetic Mean solver in lagged diffusivity method for nonlinear diffusion equations

This paper deals with the solution of nonlinear system arising from finite difference discretization of nonlinear diffusion convection equations by the lagged diffusivity functional iteration method combined with different inner iterative solvers. The analysis of the whole procedure with the splitting methods of the Arithmetic Mean(AM) and of the Alternating Group Explicit (AGE) has been developed. A comparison in terms of number of iterations has been done with the BiCG-STAB algorithm. Some numerical experiments have been carried out and they seem to show the effectiveness of the lagged diffusivity procedure with the Arithmetic Mean method as inner solver.