Integration And Cubature Methods
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Integration And Cubature Methods
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Author : Willi Freeden
language : en
Publisher: CRC Press
Release Date : 2017-11-22
Integration And Cubature Methods written by Willi Freeden 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.
In industry and economics, the most common solutions of partial differential equations involving multivariate numerical integration over cuboids include techniques of iterated one-dimensional approximate integration. In geosciences, however, the integrals are extended over potato-like volumes (such as the ball, ellipsoid, geoid, or the Earth) and their boundary surfaces which require specific multi-variate approximate integration methods. Integration and Cubature Methods: A Geomathematically Oriented Course provides a basic foundation for students, researchers, and practitioners interested in precisely these areas, as well as breaking new ground in integration and cubature in geomathematics.
Lattice Methods For Multiple Integration
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Author : I. H. Sloan
language : en
Publisher: Oxford University Press
Release Date : 1994
Lattice Methods For Multiple Integration written by I. H. Sloan and has been published by Oxford University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1994 with Mathematics categories.
This is the first book devoted to lattice methods, a recently developed way of calculating multiple integrals in many variables. Multiple integrals of this kind arise in fields such as quantum physics and chemistry, statistical mechanics, Bayesian statistics and many others. Lattice methods are an effective tool when the number of integrals are large. The book begins with a review of existing methods before presenting lattice theory in a thorough, self-contained manner, with numerous illustrations and examples. Group and number theory are included, but the treatment is such that no prior knowledge is needed. Not only the theory but the practical implementation of lattice methods is covered. An algorithm is presented alongside tables not available elsewhere, which together allow the practical evaluation of multiple integrals in many variables. Most importantly, the algorithm produces an error estimate in a very efficient manner. The book also provides a fast track for readers wanting to move rapidly to using lattice methods in practical calculations. It concludes with extensive numerical tests which compare lattice methods with other methods, such as the Monte Carlo.
The Theory Of Cubature Formulas
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Author : S.L. Sobolev
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-06-29
The Theory Of Cubature Formulas written by S.L. Sobolev 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 2013-06-29 with Mathematics categories.
This volume considers various methods for constructing cubature and quadrature formulas of arbitrary degree. These formulas are intended to approximate the calculation of multiple and conventional integrals over a bounded domain of integration. The latter is assumed to have a piecewise-smooth boundary and to be arbitrary in other aspects. Particular emphasis is placed on invariant cubature formulas and those for a cube, a simplex, and other polyhedra. Here, the techniques of functional analysis and partial differential equations are applied to the classical problem of numerical integration, to establish many important and deep analytical properties of cubature formulas. The prerequisites of the theory of many-dimensional discrete function spaces and the theory of finite differences are concisely presented. Special attention is paid to constructing and studying the optimal cubature formulas in Sobolev spaces. As an asymptotically optimal sequence of cubature formulas, a many-dimensional abstraction of the Gregory quadrature is indicated. Audience: This book is intended for researchers having a basic knowledge of functional analysis who are interested in the applications of modern theoretical methods to numerical mathematics.
Nodal Discontinuous Galerkin Methods
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Author : Jan S. Hesthaven
language : en
Publisher: Springer Science & Business Media
Release Date : 2007-12-18
Nodal Discontinuous Galerkin Methods written by Jan S. Hesthaven 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 2007-12-18 with Mathematics categories.
This book offers an introduction to the key ideas, basic analysis, and efficient implementation of discontinuous Galerkin finite element methods (DG-FEM) for the solution of partial differential equations. It covers all key theoretical results, including an overview of relevant results from approximation theory, convergence theory for numerical PDE’s, and orthogonal polynomials. Through embedded Matlab codes, coverage discusses and implements the algorithms for a number of classic systems of PDE’s: Maxwell’s equations, Euler equations, incompressible Navier-Stokes equations, and Poisson- and Helmholtz equations.
Guidance Navigation And Control For Spacecraft Rendezvous And Docking Theory And Methods
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Author : Yongchun Xie
language : en
Publisher: Springer Nature
Release Date : 2021-02-16
Guidance Navigation And Control For Spacecraft Rendezvous And Docking Theory And Methods written by Yongchun Xie and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-02-16 with Technology & Engineering categories.
This book focuses on the theory and design methods for guidance, navigation, and control (GNC) in the context of spacecraft rendezvous and docking (RVD). The position and attitude dynamics and kinematics equations for RVD are presented systematically in accordance with several different coordinate systems, including elliptical orbital frame, and recommendations are supplied on which of these equations to use in different phases of RVD. The book subsequently explains the basic principles and relative navigation algorithms of RVD sensors such as GNSS, radar, and camera-type RVD sensors. It also provides guidance algorithms and schemes for different phases of RVD, including the latest research advances in rapid RVD. In turn, the book presents a detailed introduction to intelligent adaptive control and proposes corresponding theoretical approaches to thruster configuration and control allocation for RVD. Emphasis is placed on the design method of active and passive trajectory protection in different phases of RVD, and on the safety design of the RVD mission as a whole. For purposes of verification, the Shenzhou spacecraft’s in-orbit flight mission is introduced as well. All issues addressed are described and explained from basic principles to detailed engineering methods and examples, providing aerospace engineers and students both a basic understanding of, and numerous practical engineering methods for, GNC system design in RVD.
Euclidean Design Theory
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Author : Masanori Sawa
language : en
Publisher: Springer
Release Date : 2019-07-23
Euclidean Design Theory written by Masanori Sawa and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-07-23 with Mathematics categories.
This book is the modern first treatment of experimental designs, providing a comprehensive introduction to the interrelationship between the theory of optimal designs and the theory of cubature formulas in numerical analysis. It also offers original new ideas for constructing optimal designs. The book opens with some basics on reproducing kernels, and builds up to more advanced topics, including bounds for the number of cubature formula points, equivalence theorems for statistical optimalities, and the Sobolev Theorem for the cubature formula. It concludes with a functional analytic generalization of the above classical results. Although it is intended for readers who are interested in recent advances in the construction theory of optimal experimental designs, the book is also useful for researchers seeking rich interactions between optimal experimental designs and various mathematical subjects such as spherical designs in combinatorics and cubature formulas in numerical analysis, both closely related to embeddings of classical finite-dimensional Banach spaces in functional analysis and Hilbert identities in elementary number theory. Moreover, it provides a novel communication platform for “design theorists” in a wide variety of research fields.
Numerical Solutions For Nanocomposite Structures
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Author : Maryam Shokravi
language : en
Publisher: CRC Press
Release Date : 2024-10-08
Numerical Solutions For Nanocomposite Structures written by Maryam Shokravi and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-10-08 with Technology & Engineering categories.
Numerical Solutions for Nanocomposite Structures provides an in-depth exploration of structural analysis using numerical methods grounded in rigorous mathematical modeling. Theoretical foundations are established by comprehensively elucidating theories governing beams, plates, and shells, leading to the derivation of governing equations based on the stress–strain relationship. The process of obtaining governing equations through the energy method, application of boundary conditions, and the utilization of numerical methods to calculate deflection, frequency, and buckling loads is meticulously explained, providing readers with valuable insights into structural analysis methodologies. Includes diverse numerical examples involving beams, plates, and pipes, providing a comprehensive understanding of underlying theories and relationships. Provides numerous practical examples demonstrating the application of numerical methods to address challenges in civil and mechanical engineering problems. Discusses the unique mechanical, thermal, and electrical properties of nanocomposites, and how they can be utilized in various industries.
Scientific And Engineering Computations For The 21st Century Methodologies And Applications
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Author : M. Mori
language : en
Publisher: Elsevier
Release Date : 2002-12-03
Scientific And Engineering Computations For The 21st Century Methodologies And Applications written by M. Mori and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2002-12-03 with Computers categories.
The 20th century saw tremendous achievements and progress in science and technology. Undoubtedly, computers and computer-related technologies acted as one of vital catalysts for accelerating this progress in the latter half of the century. The contributions of mathematical sciences have been equally profound, and the synergy between mathematics and computer science has played a key role in accelerating the progress of both fields as well as science and engineering. Mathematical sciences will undoubtedly continue to play this vital role in this new century. In particular, mathematical modeling and numerical simulation will continue to be among the essential methodologies for solving massive and complex problems that arise in science, engineering and manufacturing. Underpinning this all from a sound, theoretical perspective will be numerical algorithms. In recognition of this observation, this volume focuses on the following specific topics. (1) Fundamental numerical algorithms (2) Applications of numerical algorithms (3) Emerging technologies. The articles included in this issue by experts on advanced scientific and engineering computations from numerous countries elucidate state-of-the-art achievements in these three topics from various angles and suggest the future directions. Although we cannot hope to cover all the aspects in scientific and engineering computations, we hope that the articles will interest, inform and inspire members of the science and engineering community.
Crc Concise Encyclopedia Of Mathematics
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Author : Eric W. Weisstein
language : en
Publisher: CRC Press
Release Date : 2002-12-12
Crc Concise Encyclopedia Of Mathematics written by Eric W. Weisstein and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2002-12-12 with Mathematics categories.
Upon publication, the first edition of the CRC Concise Encyclopedia of Mathematics received overwhelming accolades for its unparalleled scope, readability, and utility. It soon took its place among the top selling books in the history of Chapman & Hall/CRC, and its popularity continues unabated. Yet also unabated has been the d
Numerical Methods Of Mathematical Analysis
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Author : Sh. E. Mikeladze
language : en
Publisher:
Release Date : 1961
Numerical Methods Of Mathematical Analysis written by Sh. E. Mikeladze and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1961 with Differential equations categories.