Explicit and implicit parametrizations in the construction of branching solutions by iterative methods

We give iterative methods for calculating branching solutions of nonlinear equations using explicit and implicit parametrization in a neighbourhood of a branch point. We consider the regularization problem for these schemes in the presence of errors of calculation. We construct modifications of these methods developing results in (R. Zh. Mat., 1991, 12B 1058) on the application of group analysis (R. Zh. Mat., 1988, 11B 883k) in iteration schemes in branching theory.