Manfred R. Trummer

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Pseudospectral methods are investigated for singularly perturbed boundary value problems for ordinary diierential equations which possess boundary layers. It is well known that if the boundary layer is very small then a very large number of spectral collocation points is required to obtain accurate solutions. We introduce here a new eeective procedure,(More)
Spectral collocation methods have become very useful in providing highly accurate solutions to differential equations. A straightforward implementation of these methods involves the use of spectral differentiation matrices. To obtain optimal accuracy these matrices must be computed carefully. We demonstrate that naive algorithms for computing these matrices(More)
The convergence of the additive and linear ART algorithm with relaxation is proved in a new way and under weaker assumptions on the sequence of the relaation parameters than in earlier works. These algorithms are iterative methods for the reconstruction of digitized pictures from one-dimesional views. A second proof using elementary matrix algebra shows the(More)
The ART algorithm, an iterative technique for solving large systems of linear equations, is shown to converge even for inconsistent systems, provided the relaxation parameters are chosen appropriately. The limit is a weighted least squares solution. Die Konvergenz des ART-Algorithmus, ein iteratives Verfahren zur Lösung linearer Gleichungssysteme, wird(More)
We propose an efficient preconditioning technique for the numerical solution of first-order partial differential equations (PDEs). This study has been motivated by the computation of an invariant torus of a system of ordinary differential equations. We find the torus by discretizing a nonlinear first-order PDE with a full two-dimensional Fourier spectral(More)
High-order numerical methods for solving differential equations are, in general, fairly sensitive to perturbations in their data. A previously proposed radial basis function (RBF) method, namely an integrated multiquadric scheme (IMQ), is applied to two-point boundary value problems whose solutions exhibit thin boundary layers. As frequently observed among(More)