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Numerical Integration


Numerical Integration
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Methods Of Numerical Integration


Methods Of Numerical Integration
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Author : Philip J. Davis
language : en
Publisher: Academic Press
Release Date : 2014-05-10

Methods Of Numerical Integration written by Philip J. Davis and has been published by Academic Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-05-10 with Mathematics categories.


Methods of Numerical Integration, Second Edition describes the theoretical and practical aspects of major methods of numerical integration. Numerical integration is the study of how the numerical value of an integral can be found. This book contains six chapters and begins with a discussion of the basic principles and limitations of numerical integration. The succeeding chapters present the approximate integration rules and formulas over finite and infinite intervals. These topics are followed by a review of error analysis and estimation, as well as the application of functional analysis to numerical integration. A chapter describes the approximate integration in two or more dimensions. The final chapter looks into the goals and processes of automatic integration, with particular attention to the application of Tschebyscheff polynomials. This book will be of great value to theoreticians and computer programmers.



Geometric Numerical Integration


Geometric Numerical Integration
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Author : Ernst Hairer
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-09

Geometric Numerical Integration written by Ernst Hairer and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-03-09 with Mathematics categories.


This book deals with numerical methods that preserve properties of Hamiltonian systems, reversible systems, differential equations on manifolds and problems with highly oscillatory solutions. 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 numerous figures, treats applications from physics and astronomy, and contains many numerical experiments and comparisons of different approaches.



Numerical Integration


Numerical Integration
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Author : Arnold R. Krommer
language : en
Publisher: Springer Science & Business Media
Release Date : 1994-09-28

Numerical Integration written by Arnold R. Krommer and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 1994-09-28 with Computers categories.


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.



Numerical Integration


Numerical Integration
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Author : Terje O. Espelid
language : en
Publisher: Springer Science & Business Media
Release Date : 1992

Numerical Integration written by Terje O. Espelid and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 1992 with Computers categories.


This volume contains the proceedings of the NATO Advanced Research Workshop on Numerical Integration that took place in Bergen, Norway, in June 1991. It includes papers for all invited talks and a selection of contributed talks.



A Concise Introduction To Geometric Numerical Integration


A Concise Introduction To Geometric Numerical Integration
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Author : Sergio Blanes
language : en
Publisher: CRC Press
Release Date : 2017-11-22

A Concise Introduction To Geometric Numerical Integration written by Sergio Blanes and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-11-22 with Mathematics categories.


Discover How Geometric Integrators Preserve the Main Qualitative Properties of Continuous Dynamical Systems A Concise Introduction to Geometric Numerical Integration presents the main themes, techniques, and applications of geometric integrators for researchers in mathematics, physics, astronomy, and chemistry who are already familiar with numerical tools for solving differential equations. It also offers a bridge from traditional training in the numerical analysis of differential equations to understanding recent, advanced research literature on numerical geometric integration. The book first examines high-order classical integration methods from the structure preservation point of view. It then illustrates how to construct high-order integrators via the composition of basic low-order methods and analyzes the idea of splitting. It next reviews symplectic integrators constructed directly from the theory of generating functions as well as the important category of variational integrators. The authors also explain the relationship between the preservation of the geometric properties of a numerical method and the observed favorable error propagation in long-time integration. The book concludes with an analysis of the applicability of splitting and composition methods to certain classes of partial differential equations, such as the Schrödinger equation and other evolution equations. The motivation of geometric numerical integration is not only to develop numerical methods with improved qualitative behavior but also to provide more accurate long-time integration results than those obtained by general-purpose algorithms. Accessible to researchers and post-graduate students from diverse backgrounds, this introductory book gets readers up to speed on the ideas, methods, and applications of this field. Readers can reproduce the figures and results given in the text using the MATLAB® programs and model files available online.



Numerical Integration


Numerical Integration
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Author : Philip J. Davis
language : en
Publisher:
Release Date : 1967

Numerical Integration written by Philip J. Davis and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1967 with Numerical integration categories.




Computerized Numerical Integration


Computerized Numerical Integration
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Author : D. G. KItzinger
language : en
Publisher:
Release Date : 1967

Computerized Numerical Integration written by D. G. KItzinger and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1967 with Numerical integration categories.




Quadrature Theory


Quadrature Theory
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Author : Helmut Brass
language : en
Publisher: American Mathematical Soc.
Release Date : 2011-10-12

Quadrature Theory written by Helmut Brass and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-10-12 with Mathematics categories.


Every book on numerical analysis covers methods for the approximate calculation of definite integrals. The authors of this book provide a complementary treatment of the topic by presenting a coherent theory of quadrature methods that encompasses many deep and elegant results as well as a large number of interesting (solved and open) problems. The inclusion of the word ``theory'' in the title highlights the authors' emphasis on analytical questions, such as the existence and structure of quadrature methods and selection criteria based on strict error bounds for quadrature rules. Systematic analyses of this kind rely on certain properties of the integrand, called ``co-observations,'' which form the central organizing principle for the authors' theory, and distinguish their book from other texts on numerical integration. A wide variety of co-observations are examined, as a detailed understanding of these is useful for solving problems in practical contexts. While quadrature theory is often viewed as a branch of numerical analysis, its influence extends much further. It has been the starting point of many far-reaching generalizations in various directions, as well as a testing ground for new ideas and concepts. The material in this book should be accessible to anyone who has taken the standard undergraduate courses in linear algebra, advanced calculus, and real analysis.



Practical Numerical Integration


Practical Numerical Integration
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Author : Gwynne Evans
language : en
Publisher:
Release Date : 1993-08-24

Practical Numerical Integration written by Gwynne Evans and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1993-08-24 with Mathematics categories.


Offers the quadrature user a selection of the most effective algorithms in each of the main areas of the subject. Topics range from Simpson's rule and Gaussian quadrature to recent research on irregular oscillatory and singular quadrature. A full set of test examples is given and implemented for each method discussed, demonstrating its practical limitations.



Computational Integration


Computational Integration
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Author : Arnold R. Krommer
language : en
Publisher: SIAM
Release Date : 1998-01-01

Computational Integration written by Arnold R. Krommer and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 1998-01-01 with Mathematics categories.


This survey covers a wide range of topics fundamental to calculating integrals on computer systems and discusses both the theoretical and computational aspects of numerical and symbolic methods. It includes extensive sections on one- and multidimensional integration formulas, like polynomial, number-theoretic, and pseudorandom formulas, and deals with issues concerning the construction of numerical integration algorithms.