Mathematics – Numerical Analysis
Scientific paper
2007-10-04
Mathematics
Numerical Analysis
32 pages, 17 figures
Scientific paper
We present a new numerical method for computing the pure-point spectrum associated with the linear stability of coherent structures. In the context of the Evans function shooting and matching approach, all the relevant information is carried by the flow projected onto the underlying Grassmann manifold. We show how to numerically construct this projected flow in a stable and robust manner. In particular, the method avoids representation singularities by, in practice, choosing the best coordinate patch representation for the flow as it evolves. The method is analytic in the spectral parameter and of complexity bounded by the order of the spectral problem cubed. For large systems it represents a competitive method to those recently developed that are based on continuous orthogonalization. We demonstrate this by comparing the two methods in three applications: Boussinesq solitary waves, autocatalytic travelling waves and Ekman boundary layer.
Ledoux Veerle
Malham Simon J. A.
Thümmler Vera
No associations
LandOfFree
Grassmannian spectral shooting does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Grassmannian spectral shooting, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Grassmannian spectral shooting will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-563572