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A finite difference scheme for computing inertial manifolds. (English) Zbl 0824.65125

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.

MSC:

65Z05 Applications to the sciences
65M06 Finite difference methods for initial value and initial-boundary value problems involving PDEs
65N25 Numerical methods for eigenvalue problems for boundary value problems involving PDEs
35K55 Nonlinear parabolic equations

Software:

AUTO
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References:

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