Titlebook: Large Scale Scientific Computing; P. Deuflhard,B. Engquist Book 1987 Birkh?user Boston 1987 Mathematica.algorithms.boundary element method

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Extrapolation Integrators for Quasilinear Implicit ODEs Extensions to problems with index = 1, where B is singular, are also included. In large scale scientific computing, problems of the type (0.1) may arise e.g. in chemical reaction kinetics, when thermodynamic equations are added, or in method of lines treatment for time-dependent PDEs with moving spatial grids (compare Miller [8,9], Hyman [6]).

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Computing Bifurcation Diagrams for Large Nonlinear Variational Problemsal type. Included are techniques to find a point on a branch, to trace solution branches, to detect singularities, to compute turning points, simple and double nondegenerate bifurcation points and to calculate emanating directions from bifurcation points. The perfor-mance of the method is demonstrated at two examples.

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Numerical Backprojection in the Inverse 3D Radon Transformmula. Using special functions we demonstrate that, if suitable filters in the first reconstruction step — differenciation of order two — are used, essential errors are produced only outside the region of interest. The directions needed in measuring the data fulfil also another requirement, they guarantee optimal resolution in the reconstruction.

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Vortex Dynamics Studied by Large-Scale Solutions to the Euler Equations like the singular points. Several flow problems designed to test the vortex-sheet hypothesis are solved upon a mesh with over 600,000 grid cells. These solutions, even when the body is smooth, present numerical observations of such vortex sheets and singular points which support the hypothesis. One