A finite difference scheme for computing inertial manifolds (Q1894291)

A simple method is described for computing the inertial manifold of dissipative partial differential equations, the range of applications of which is rather large. The basic feature of the approach is to show that good approximations to first few eigenvalues and eigenvectors needed in inertial manifold computations can be readily obtained by an inverse Lanczos iteration without having to compute the complete eigensystem. After some theoretical background, the method is explained with the Kuramoto-Sivashinsky equation as example, and the numerical results are displayed.