Numerical Integration
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Numerical Integration
Author: Arnold R. Krommer
language: en
Publisher: Springer Science & Business Media
Release Date: 1994-09-28
The topics in this volume constitute a fitting tribute by distinguished physicists and mathematicians. They cover strings, conformal field theories, W and Virasoro algebras, topological field theory, quantum groups, vertex and Hopf algebras, and non-commutative geometry. The relatively long contributions are pedagogical in style and address students as well as scientists.
Geometric Numerical Integration
Author: Ernst Hairer
language: en
Publisher: Springer Science & Business Media
Release Date: 2013-03-09
Numerical methods that preserve properties of Hamiltonian systems, reversible systems, differential equations on manifolds and problems with highly oscillatory solutions are the subject of this book. A complete self-contained theory of symplectic and symmetric methods, which include Runge-Kutta, composition, splitting, multistep and various specially designed integrators, is presented and their construction and practical merits are discussed. The long-time behaviour of the numerical solutions is studied using a backward error analysis (modified equations) combined with KAM theory. The book is illustrated by many figures, it treats applications from physics and astronomy and contains many numerical experiments and comparisons of different approaches.
Numerical Integration
Author: T.O. Espelid
language: en
Publisher: Springer Science & Business Media
Release Date: 2012-12-06
This volume contains refereed papers and extended abstracts of papers presented at the NATO Advanced Research Workshop entitled 'Numerical Integration: Recent Develop ments, Software and Applications', held at the University of Bergen, Bergen, Norway, June 17-21,1991. The Workshop was attended by thirty-eight scientists. A total of eight NATO countries were represented. Eleven invited lectures and twenty-three contributed lectures were presented, of which twenty-five appear in full in this volume, together with three extended abstracts and one note. The main focus of the workshop was to survey recent progress in the theory of methods for the calculation of integrals and show how the theoretical results have been used in software development and in practical applications. The papers in this volume fall into four broad categories: numerical integration rules, numerical integration error analysis, numerical integration applications and numerical integration algorithms and software. It is five years since the last workshop of this nature was held, at Dalhousie University in Halifax, Canada, in 1986. Recent theoretical developments have mostly occurred in the area of integration rule construction. For polynomial integrating rules, invariant theory and ideal theory have been used to provide lower bounds on the numbers of points for different types of multidimensional rules, and to help in structuring the nonlinear systems which must be solved to determine the points and weights for the rules. Many new optimal or near optimal rules have been found for a variety of integration regions using these techniques.