Mathematics – Numerical Analysis
Scientific paper
2001-01-25
Mathematics
Numerical Analysis
8 pages, LaTeX
Scientific paper
10.1016/S0010-4655(01)00359-9
Modern dynamical systems theory has previously had little to say about finite difference and finite element approximations of partial differential equations (Archilla, 1998). However, recently I have shown one way that centre manifold theory may be used to create and support the spatial discretisation of \pde{}s such as Burgers' equation (Roberts, 1998a) and the Kuramoto-Sivashinsky equation (MacKenzie, 2000). In this paper the geometric view of a centre manifold is used to provide correct initial conditions for numerical discretisations (Roberts, 1997). The derived projection of initial conditions follows from the physical processes expressed in the PDEs and so is appropriately conservative. This rational approach increases the accuracy of forecasts made with finite difference models.
No associations
LandOfFree
Holistic projection of initial conditions onto a finite difference approximation 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 Holistic projection of initial conditions onto a finite difference approximation, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Holistic projection of initial conditions onto a finite difference approximation will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-64816