Spectral Methods with Sparse Matrices.
Konvergenzaussagen für Kollokationsverfahren bei elliptischen Randwertaufgaben.
Spectral methods for singular perturbation problems
We study spectral discretizations for singular perturbation problems. A special technique of stabilization for the spectral method is proposed. Boundary layer problems are accurately solved by a domain decomposition method. An effective iterative method for the solution of spectral systems is proposed. Suitable components for a multigrid method are presented.
Strong convergence estimates for pseudospectral methods
Strong convergence estimates for pseudospectral methods applied to ordinary boundary value problems are derived. The results are also used for a convergence analysis of the Schwarz algorithm (a special domain decomposition technique). Different types of nodes (Chebyshev, Legendre nodes) are examined and compared.
Einschliessungsaussagen bei Systemen semilinearer parabolischer Differentialgleichungen
Für die Lösungen seminlinearer parabolischer Differentialgleichungen werden Einschliessungsaussagen hergeleitet. Hierbei werden Aussagen zur Stabilität von Lösungen ermittelt. Die Resultate werden am Beispiel der Fitzhugh-Nagumo Gleichungen diskutiert.
Some results about the pseudospectral approximation of one-dimensional fourth-order problems.
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