Preprint of the project:
05-017 Vera Thümmler.
Numerical approximation of relative equilibria for equivariant PDEs
In this paper we prove convergence results for the numerical
approximation of relative equilibria of equivariant evolution
equations with finite differences on an finite equidistant grid with
appropriate boundary conditions. Moreover, we consider the
approximation of isolated eigenvalues of finite multiplicity of the
linear operator which arises from linearization at the equilibrium as
well as the approximation of the corresponding invariant subspace. The
results in this paper are illustrated by numerical computations for the quintic complex
Ginzburg Landau equation.
