On representation of solutions to nonlinear partial differential equations by new constructions of consistent special series (Q2773655)

New constructions of consistent special series for representation of solutions to nonlinear partial differential equations are presented. This approach is the continuation of the special series method. The main feature of this method is constructive representation of solutions to nonlinear equations in the form of a series on the powers of ``basic'' functions with recurrently calculated coefficients found from solutions to ordinary differential equations. It is shown that these series can be used for solving initial-boundary value problems. The convergence area of the series proposed is investigated and results of numerical experiments are presented.