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This book provides useful reference material for those concerned with the use of Fourier analysis and computational fluid dynamics.
Fourrier analysis of the accuracy of semi-discretizations. Higher order semi-discretizations. Full discretizations. Damping, diffusion and filtering. Group velocity. Time-Fourier transforms. Fourier analysis and L2-norm of the global error. Spectral methods. Equations in two dimensions: anisotropy.
These proceedings collect lectures given at ENUMATH 2005, the 6th European Conference on Numerical Mathematics and Advanced Applications held in Santiago de Compostela, Spain in July, 2005. Topics include applications such as fluid dynamics, electromagnetism, structural mechanics, interface problems, waves, finance, heat transfer, unbounded domains, numerical linear algebra, convection-diffusion, as well as methodologies such as a posteriori error estimates, discontinuous Galerkin methods, multiscale methods, optimization, and more.
The present book is an edition of the manuscripts to the courses "Numerical Methods I" and "Numerical Mathematics I and II" which Professor H. Rutishauser held at the E.T.H. in Zurich. The first-named course was newly conceived in the spring semester of 1970, and intended for beginners, while the two others were given repeatedly as elective courses in the sixties. For an understanding of most chapters the funda mentals of linear algebra and calculus suffice. In some places a little complex variable theory is used in addition. However, the reader can get by without any knowledge of functional analysis. The first seven chapters discuss the direct solution of systems of linear equations, the solution of nonlinear systems, least squares prob lems, interpolation by polynomials, numerical quadrature, and approxima tion by Chebyshev series and by Remez' algorithm. The remaining chapters include the treatment of ordinary and partial differential equa tions, the iterative solution of linear equations, and a discussion of eigen value problems. In addition, there is an appendix dealing with the qd algorithm and with an axiomatic treatment of computer arithmetic.
A study of the art and science of solving elliptic problems numerically, with an emphasis on problems that have important scientific and engineering applications, and that are solvable at moderate cost on computing machines.
Differential equations are the pre-eminent modelling device of engineering and the applied sciences. This volume contains a refereed subset of papers presented at the 1991 IMACS World Congress. A natural subdivision occurred - General Theory, Specific Differential Equations and Computational Methods. There are eleven papers in the area termed General Theory. Seventeen papers concern Specific Differential Equations - both ordinary and partial - which have been used to model various phenomena. Finally, fourteen papers are devoted to a variety of Computational Methods.

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