On the general problem of formulation and optimization of a p-parametric extrapolated alternating direction implicit scheme

AbstractIn this paper we formulate the most general Extrapolated (E). A.D.I. scheme for the numerical solution of an elliptic partial differential equation. We then consider the problem of minimization of the spectral radius of the iterative matrix arising and after a brief reference to previous works in this area we solve the problem theoretically in a special, though still a quite, general case. Thus we are able to prove that all the well known monoparametric or biparametric E.A.D.I. schemes can be accelerated straightforward. Finally we give a list of problems, whose rates of convergence can be improved on by the new general method we propose, as well as appropriate references