Abstract
Modern dynamical systems theory has previously had little to say about finite difference and finite element approximations of partial differential equations ( pdes) [B. Garcı́a-Archilla, E.S. Titi, SIAM J. Numer. Anal. 37 (2000) 470–499]. However, recently I have shown one way that centre manifold theory may be used to create and support the spatial discretization of pdes such as Burgers' equation [A.J. Roberts, Appl. Numer. Modelling 37 (2001) 371–396] and the Kuramoto–Sivashinsky equation [T. Mackenzie, A.J. Roberts, ANZIAM J. 42 (E) (2000) C918–C935]. In this paper the geometric view of a centre manifold is used to provide correct initial conditions for numerical discretizations [A.J. Roberts, Comput. Phys. Comm. 126 (3) (2000) 187–206]. 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.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
