Moreover, explicit form of modern extrapolation methods does not allow them to be applicable for solving stiff problems. In the paper we construct the theory of implicit extrapolation methods and show how such methods work in practice. We also discuss problems concerning implementation of implicit methods because we cannot actually find the approximate solution from an implicit method exactly. We have to use an iterative method to solve the nonlinear algebraic system arising from application of an implicit method to the original problem. But the additional error from the iterative method may influence the asymptotic expasion of the global error and, hence, the behavior of the extrapolation method.
Numerical experiments support the theoretical resalts of the paper.