Iterative method of analysis for nonlinear singularly perturbed initial and boundary value problems (Q1589008)

The author obtains results concerning the existence of a unique bounded solution to a class of regular and singularly perturbed nonlinear initial and boundary value problems. An asymptotic decomposition of the solution to singularly perturbed multipoint boundary value problems with weak nonlinearity is done by means of special matrix transformations and an iterative method. It is shown that the solution is valid in the absence of resonance correlations and in the presence of both identical and nonidentical resonances. The new algorithm is convenient for numerical realization. It distinguishes the singularities of the solution in a closed analytic form.