APPROXIMATE INERTIAL MANIFOLDS FOR THE KURAMOTO-SIVASHINSKY EQUATION - ANALYSIS AND COMPUTATIONS Academic Article

abstract

• We evaluate several alternative methods for the approximation of inertial manifolds for the one-dimensional Kuramoto-Sivashinsky equation (KSE). A method motivated by the dynamics originally developed for the Navier-Stokes equation is adapted for the KSE. Rigorous error estimates are obtained and compared to those of other methods introduced in the literature. Formal relationships between these other methods and the one introduced here are established. Numerical bifurcation diagrams of the various approximate inertial forms for the KSE are presented. We discuss the correspondence between the rigorous error estimates and the accuracy of the computational results. These methods can be adapted to other dissipative partial differential equations. 1990.

authors

• Titi, Edriss

published proceedings

• PHYSICA D

author list (cited authors)

• JOLLY, M. S., KEVREKIDIS, I. G., & TITI, E. S.

citation count

• 187

complete list of authors

• JOLLY, MS||KEVREKIDIS, IG||TITI, ES

publication date

• August 1990

publisher

• Elsevier  Publisher

published in

• Physica D : Non-linear phenomena  Journal

keywords

• 49 Mathematical Sciences
• 4903 Numerical And Computational Mathematics

Digital Object Identifier (DOI)

• 10.1016/0167-2789(90)90046-R

start page

• 38

end page

• 60

volume

• 44

issue

• 1-2

URL

• http://dx.doi.org/10.1016/0167-2789(90)90046-r