Title: A multiscale method for highly oscillatory dynamical systems using a Poincaré map type technique
Typically, application of averaging methods requires identification of a change of variables that splits the system into slow and fast coordinates. However, in many examples such a transformation is unknown or difficult to compute. The talk will describe a numerical multiscale method that approximates the slow variables of a highly oscillatory system without explicitly finding it. The proposed method constructs an effective path in the state space whose projection onto the slow subspace has the correct dynamics. A novel on-the-fly filtering technique provides high order accuracy.