On the nonlinear acceleration of iterative schemes

Consideration is given to the problem of constructing nonstationary schemes that do not necessarily have a physical interpretation, which converge faster than those with physical solutions, in the solution of stationary problems by the relaxation method. The use of artificial viscosity in the solution of the Navier-Stokes equations is examined, and the convergence rate of incomplete iterative approximation schemes is discussed. Results are then presented of numerical computations of a finite-difference Dirichlet problem which were performed using three incomplete approximation schemes, and it is shown that all three schemes converge faster than the schemes from which they were constructed and faster than the two-cycle implicit Richardson scheme.