Periodical solutions of nonlinear dynamical systems by decompositon method (Q1106026)

In the field of nonlinear mechanics, the Adomian decomposition method [e.g.: \textit{G. Adomian}, Nonlinear stochastic operator equations (1986; Zbl 0609.60072)] has been recently developed and applied with satisfactory results for determining in approximate analytical form the solution of initial value problems for ordinary differential equations, mixed initial-boundary value problems and partial differential equations. This paper deals with the applicability of the said method to determine the periodical, steady-state response of nonlinear oscillating systems. A suitable adaptation of Adomian's procedure is developed, which yields the approximate expressions of the harmonic oscillations, obtained by easy calculations even in the case of high nonlinearity. An application concerning a well-known problem in nonlinear mechanics is considered, with pertinent comparisons with perturbations and numerical techniques.