A collection of papers on recent progress in the development of numerical applications with automatic result verification. The book includes various applications of enclosure methods to problems in the engineering sciences, such as MHD flow calculations and KKR bandstructure calculations.
Author(s): E. Adams and U. Kulisch (Eds.)
Series: Mathematics in Science and Engineering 189
Publisher: Academic Press
Year: 1993
Language: English
Pages: iii-x, 1-612
Content:
Edited by
Page iii
Copyright page
Page iv
Contributors
Page vii
Preface
Pages ix-x
Acknowledgements
Page x
Dedication
Page x
E. Adams, U. Kulisch
Introduction
Pages 1-12
E. Adams, U. Kulisch
PASCAL-XSC New Concepts for Scientific Computation and Numerical Data Processing Original Research Article
Pages 15-44
R. Hammer, M. Neaga, D. Ratz
ACRITH-XSC A Fortran—like Language for Verified Scientific Computing Original Research Article
Pages 45-70
Wolfgang V. Walter
C-XSC A Programming Environment for Verified Scientific Computing and Numerical Data Processing Original Research Article
Pages 71-86
Christian Lawo
Proposal for Accurate Floating-Point Vector Arithmetic Original Research Article
Pages 87-102
G. Bohlender, D. Cordes, A. Knöfel, U. Kulisch, R. Lohner, W.V. Walter
Automatic Differentiation and Applications Original Research Article
Pages 105-142
Hans-Christoph Fischer
Numerical Quadrature by Extrapolation with Automatic Result Verification Original Research Article
Pages 143-185
Rainer Kelch
Numerical Integration in Two Dimensions with Automatic Result Verification Original Research Article
Pages 187-224
Ulrike Storck
Verified Solution of Integral Equations with Applications Original Research Article
Pages 225-253
Hans-Jürgen Dobner
Enclosure Methods for Linear and Nonlinear Systems of Fredholm Integral Equations of the Second Kind Original Research Article
Pages 255-282
Wolfram Klein
A Step Size Control for Lohner's Enclosure Algorithm for Ordinary Differential Equations with Initial Conditions Original Research Article
Pages 283-299
W. Rufeger, E. Adams
Interval Arithmetic in Staggered Correction Format Original Research Article
Pages 301-321
Rudolf J. Lohner
Multiple-Precision Computations with Result Verification Original Research Article
Pages 325-356
Walter Krämer
Verification of Asymptotic Stability for Interval Matrices and Applications in Control Theory Original Research Article
Pages 357-395
Beate Gross
Numerical Reliability of MHD Flow Calculations Original Research Article
Pages 397-421
Wera U. Klein
The Reliability Question for Discretizations of Evolution Problems Original Research Article
Pages 423-526
Ernst Adams
KKR Bandstructure Calculations, A Challenge to Numerical Accuracy Original Research Article
Pages 527-547
R. Schütz, H. Winter, G. Ehret
A Hardware Kernel for Scientific/Engineering Computations Original Research Article
Pages 549-570
Andreas Knöfel
Bibliography on Enclosure Methods and Related Topics Original Research Article
Pages 571-608
Gerd Bohlender
Index
Pages 609-612
