Power series expansions of discretization errors for nonlinear funtional equations

Sufficient conditions are given under which discretization errors for numerical methods applied to nonlinear functional equations possess power series expansions of a special form. The conditions are quite general and are applicable, for example, to problems whose solutions are only mildly smooth, i.e., low-order derivatives of the solutions are discontinuous. It is argued that Richardson extrapolation can be applied to numerical methods that possess such error expansions. Several numerical examples are presented that illustrate application of the conditions.