New methods for calculating the stability of periodic solutions

AbstractSystems of autonomous first-order ordinary differential equations are considered (dimension n). The stability of periodic solutions is determined by the eigenvalues of the monodromy matrix M. A standard way of calculating M requires storage proportional to n2. In this paper, new algorithms for calculating M are proposed. One algorithm requires storage proportional to n, another algorithm involves nearly no work, provided the periodic solution was calculated by shooting. Features of the new algorithms are discussed