Higher-order averaging: periodic solutions, linear systems and an application Original Research Article

Existence and stability of periodic solutions by using second-order averaging when the vector field by first-order averaging vanishes, will be studied in this paper as well as its generalization to higher order. A special averaging algorithm for the computation of higher approximations of the fundamental matrix of linear equations with periodic coefficients is given. As an application the existence and stability of periodic solutions of an inhomogeneous second-order equation with time-dependent damping coefficient are studied.