We propose algorithms that allow for nonlinear equations to obtain asymptotic expansions of solutions in the form of: (a) power series with constant coefficients, (b) power series with coefficients which are power series of logarithm and (c) power series of exponent of a power series with coefficients which are power series as well. These algorithms are applicable to nonliner equations (A) algebraic, (B) ordinary differential and (C) partial differential, and to systems of such equations as well. We give the description of the method for one ordinary differential equation and we enumerate some applications of these algorithms.

expansions of solutions to ODE, power expansions, complicated expansions, exponential expansions

Mathematical modelling in actual problems of science and technics

Bruno Alexander Dmitrievich,  ,  orcid.org/0000-0002-7465-1258,  KIAM RAS