Projective and Coarse Projective Integration for Problems with Continuous Symmetries

Details Projective and Coarse Projective Integration for Problems with Continuous Symmetries Projective and Coarse Projective Integration for Problems with Continuous Symmetries

2006-08-04

arxiv.org/abs/math/0608122v1

Mathematics

Dynamical Systems

Scientific paper

10.1016/j.jcp.2006.12.003

Temporal integration of equations possessing continuous symmetries (e.g. systems with translational invariance associated with traveling solutions and scale invariance associated with self-similar solutions) in a ``co-evolving'' frame (i.e. a frame which is co-traveling, co-collapsing or co-exploding with the evolving solution) leads to improved accuracy because of the smaller time derivative in the new spatial frame. The slower time behavior permits the use of {\it projective} and {\it coarse projective} integration with longer projective steps in the computation of the time evolution of partial differential equations and multiscale systems, respectively. These methods are also demonstrated to be effective for systems which only approximately or asymptotically possess continuous symmetries. The ideas of projective integration in a co-evolving frame are illustrated on the one-dimensional, translationally invariant Nagumo partial differential equation (PDE). A corresponding kinetic Monte Carlo model, motivated from the Nagumo kinetics, is used to illustrate the coarse-grained method. A simple, one-dimensional diffusion problem is used to illustrate the scale invariant case. The efficiency of projective integration in the co-evolving frame for both the macroscopic diffusion PDE and for a random-walker particle based model is again demonstrated.

Affiliated with

Also associated with

No associations

Rating

Projective and Coarse Projective Integration for Problems with Continuous Symmetries 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 Projective and Coarse Projective Integration for Problems with Continuous Symmetries, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Projective and Coarse Projective Integration for Problems with Continuous Symmetries will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-49517