A FINITE-DIFFERENCE SCHEME FOR COMPUTING INERTIAL MANIFOLDS

A fully discrete method is presented for computing inertial manifolds of dissipative partial differential equations. In particular, only an approximate spectral decomposition of the dominant differential operat or needs to be known, The first few of the smallest eigenvalues and ei genvectors of the discretized operator are approximated using the Lanc zos algorithm, Numerical experiments are performed for an equation in one space dimension by discretizing tile space variable on a sufficien tly fine grid. The basic ideas and techniques are exemplified for sele cted bifurcation diagrams of an integrated form of the Kuramoto-Sivash insky equation.