Validation Numerics
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Validation Numerics
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Author : R. Albrecht
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Validation Numerics written by R. Albrecht 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 2012-12-06 with Mathematics categories.
The articles in this book give a comprehensive overview on the whole field of validated numerics. The problems covered include simultaneous systems of linear and nonlinear equations, differential and integral equations and certain applications from technical sciences. Furthermore some papers which improve the tools are included. The book is a must for scientists working in numerical analysis, computer science and in technical fields.
Numerical Verification Methods And Computer Assisted Proofs For Partial Differential Equations
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Author : Mitsuhiro T. Nakao
language : en
Publisher: Springer Nature
Release Date : 2019-11-11
Numerical Verification Methods And Computer Assisted Proofs For Partial Differential Equations written by Mitsuhiro T. Nakao and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-11-11 with Mathematics categories.
In the last decades, various mathematical problems have been solved by computer-assisted proofs, among them the Kepler conjecture, the existence of chaos, the existence of the Lorenz attractor, the famous four-color problem, and more. In many cases, computer-assisted proofs have the remarkable advantage (compared with a “theoretical” proof) of additionally providing accurate quantitative information. The authors have been working more than a quarter century to establish methods for the verified computation of solutions for partial differential equations, mainly for nonlinear elliptic problems of the form -∆u=f(x,u,∇u) with Dirichlet boundary conditions. Here, by “verified computation” is meant a computer-assisted numerical approach for proving the existence of a solution in a close and explicit neighborhood of an approximate solution. The quantitative information provided by these techniques is also significant from the viewpoint of a posteriori error estimates for approximate solutions of the concerned partial differential equations in a mathematically rigorous sense. In this monograph, the authors give a detailed description of the verified computations and computer-assisted proofs for partial differential equations that they developed. In Part I, the methods mainly studied by the authors Nakao and Watanabe are presented. These methods are based on a finite dimensional projection and constructive a priori error estimates for finite element approximations of the Poisson equation. In Part II, the computer-assisted approaches via eigenvalue bounds developed by the author Plum are explained in detail. The main task of this method consists of establishing eigenvalue bounds for the linearization of the corresponding nonlinear problem at the computed approximate solution. Some brief remarks on other approaches are also given in Part III. Each method in Parts I and II is accompanied by appropriate numerical examples that confirm the actual usefulness of the authors’ methods. Also in some examples practical computer algorithms are supplied so that readers can easily implement the verification programs by themselves.
Self Validating Numerics For Function Space Problems
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Author : Edgar W. Kaucher
language : en
Publisher:
Release Date : 1984
Self Validating Numerics For Function Space Problems written by Edgar W. Kaucher and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1984 with Mathematics categories.
Mathematics of Computing -- Numerical Analysis.
Scientific Computing And Validated Numerics
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Author : G. Alefeld
language : en
Publisher: De Gruyter Akademie Forschung
Release Date : 1996
Scientific Computing And Validated Numerics written by G. Alefeld and has been published by De Gruyter Akademie Forschung this book supported file pdf, txt, epub, kindle and other format this book has been release on 1996 with Mathematics categories.
The International Symposium on Scientific Computing, Computer Arithmetic and Validated Numerics SCAN is held biannually, the fourth conference took place in Wuppertal 1995. This volume contains contributions from outstanding research specialists based on their presentations at SCAN-95. It covers all aspects of scientific computing with validation, starting with the latest developments in the design of floating point units together with algorithms for floating point operations and elementary function evaluations with maximum accuracy. The book continues by treating scientific computing methods for many areas of applied mathematics such as numerical linear algebra, nonlinear equations, global optimization, ordinary and partial differential equations and dynamical systems. Some computer science aspects like complexity are also considered as are examples where validation methods have successfully be used in applications from the engineering sciences.
Validation Of Three Dimensional Incompressible Spatial Direct Numerical Simulation Code A Comparison With Linear Stability And Parabolic Stability Equation Theories For Boundary Layer Transition On A Flat Plate
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Author : Ronald D. Joslin
language : en
Publisher:
Release Date : 1992
Validation Of Three Dimensional Incompressible Spatial Direct Numerical Simulation Code A Comparison With Linear Stability And Parabolic Stability Equation Theories For Boundary Layer Transition On A Flat Plate written by Ronald D. Joslin and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1992 with categories.
Validation Of A Numerical Model For Prediction Of Moisture Content For Binary Mixtures Of Corn Oats And Wheat Cereals In Semipermeable Packaging
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Author : Carlos Gustavo Castro Izaguirre
language : en
Publisher:
Release Date : 2001
Validation Of A Numerical Model For Prediction Of Moisture Content For Binary Mixtures Of Corn Oats And Wheat Cereals In Semipermeable Packaging written by Carlos Gustavo Castro Izaguirre and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2001 with Cereals, Prepared categories.
Experimental Validation Testing Of Numerical Prediction Techniques For Three Dimensional Fracture And Fatigue
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Author : William T. Riddell
language : en
Publisher:
Release Date : 1995
Experimental Validation Testing Of Numerical Prediction Techniques For Three Dimensional Fracture And Fatigue written by William T. Riddell and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1995 with Fracture mechanics categories.
A crack does not always preclude safe use of a structure. Nearly all matter contains flaws at some scale. Therefore, we will find a crack in almost any structure if we look hard enough. With this in mind, a more logical response to a cracked structure is to ask "will this crack affect the use and/or safety of this structure?" We need to understand fracture mechanics to answer this question, which is the heart of damage tolerant design.
Verification Validation And Solution Quality In Computational Physics Cfd Methods Applied To Ice Sheet Physics
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Author :
language : en
Publisher:
Release Date : 2005
Verification Validation And Solution Quality In Computational Physics Cfd Methods Applied To Ice Sheet Physics written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005 with categories.
Validation Numerics
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Author : R. Albrecht
language : en
Publisher: Springer
Release Date : 1993-05-11
Validation Numerics written by R. Albrecht and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 1993-05-11 with Mathematics categories.
The articles in this book give a comprehensive overview on the whole field of validated numerics. The problems covered include simultaneous systems of linear and nonlinear equations, differential and integral equations and certain applications from technical sciences. Furthermore some papers which improve the tools are included. The book is a must for scientists working in numerical analysis, computer science and in technical fields.
Verification Model Checking And Abstract Interpretation
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Author :
language : en
Publisher:
Release Date : 2005
Verification Model Checking And Abstract Interpretation written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005 with Computer programs categories.