Integral Methods in Science and Engineering.pdf

(2686 KB) Pobierz
Integral Methods in
Science and Engineering
Theoretical and
Practical Aspects
C. Constanda
Z. Nashed
D. Rollins
Editors
Birkhauser
Boston • Basel • Berlin
C. Constanda
University of Tulsa
Department of Mathematical
and Computer Sciences
600 South College Avenue
Tulsa, OK 74104
USA
Z. Nashed
University of Central Florida
Department of Mathematics
4000 Central Florida Blvd.
Orlando, FL 32816
USA
D. Rollins
University of Central Florida
Department of Mathematics
4000 Central Florida Blvd.
Orlando, FL 32816
USA
Cover design by Alex Gerasev.
AMS Subject Classification: 45-06, 65-06, 74-06, 76-06
Library of Congress Cataloging-in-Publication Data
Integral methods in science and engineering : theoretical and practical aspects / C.
Constanda, Z. Nashed, D. Rollins (editors).
p. cm.
Includes bibliographical references and index.
ISBN 0-8176-4377-X (alk. paper)
1. Integral equations–Numerical solutions–Congresses. 2. Mathematical
analysis–Congresses. 3. Science–Mathematics–Congresses. 4. Engineering
mathematics–Congresses. I. Constanda, C. (Christian) II. Nashed, Z. (Zuhair) III. Rollins,
D. (David), 1955-
QA431.I49 2005
518 .66–dc22
2005053047
ISBN
-10:
0-8176-4377-X
e
-
ISBN
:
0-8176-4450-4
Printed on acid-free paper.
ISBN-13
:
978-0-8176-4377-5
2006 Birkhauser Boston
All rights reserved. This work may not be translated or copied in whole or in part without the writ-
ten permission of the publisher (Birkhauser Boston, c/o Springer Science + Business Media Inc., 233
Spring Street, New York, NY 10013, USA) and the author, except for brief excerpts in connection
with reviews or scholarly analysis. Use in connection with any form of information storage and re-
trieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known
or hereafter developed is forbidden.
The use in this publication of trade names, trademarks, service marks and similar terms, even if they
are not identified as such, is not to be taken as an expression of opinion as to whether or not they are
subject to proprietary rights.
c
Printed in the United States of America.
(IBT)
987654321
www.birkhauser.com
762859907.001.png 762859907.002.png 762859907.003.png
Contents
Preface
xi
Contributors
xiii
1
Newton-type Methods for Some Nonlinear Differential
Problems
Mario Ahues and Alain Largillier
1
1.1 TheGeneralFramework ..............
1
1.2
Nonlinear Boundary Value Problems
.........
6
1.3 SpectralDifferentialProblems ............
9
1.4
Newton Method for the Matrix Eigenvalue Problem
. .
13
References
....................
14
2
Nodal and Laplace Transform Methods for Solving
2D Heat Conduction
Ivanilda B. Aseka, Marco T. Vilhena,
and Haroldo F. Campos Velho
17
2.1 Introduction
...................
17
2.2
Nodal Method in Multi-layer Heat Conduction
....
18
2.3 NumericalResults .................
24
2.4 FinalRemarks...................
26
References
....................
27
3
The Cauchy Problem in the Bending of
Thermoelastic Plates
Igor Chudinovich and Christian Constanda
29
3.1 Introduction
...................
29
3.2 Prerequisites
...................
29
3.3 HomogeneousSystem................
32
3.4 HomogeneousInitialData..............
33
References
....................
35
4
Mixed Initial-boundary Value Problems for
Thermoelastic Plates
Igor Chudinovich and Christian Constanda
37
4.1 Introduction
...................
37
4.2 Prerequisites
...................
37
4.3 TheParameter-dependentProblems .........
39
vi
Contents
4.4 TheMainResults .................
43
References
....................
45
5
On the Structure of the Eigenfunctions of a
Vibrating Plate with a Concentrated Mass and Very
Small Thickness
Delfina Gomez, Miguel Lobo, and Eugenia Perez
47
5.1 IntroductionandStatementoftheProblem ......
47
5.2
Asymptotics in the Case r =1............
50
5.3
Asymptotics in the Case r> 1............
56
References
....................
58
6
A Finite-dimensional Stabilized Variational Method
for Unbounded Operators
Charles W. Groetsch
61
6.1 Introduction
...................
61
6.2 Background ....................
63
6.3 TheTikhonov–MorozovMethod ...........
64
6.4 AnAbstractFiniteElementMethod .........
65
References
....................
70
7
A Converse Result for the Tikhonov–Morozov Method
Charles W. Groetsch
71
7.1 Introduction
...................
71
7.2 TheTikhonov–MorozovMethod ...........
73
7.3 OperatorswithCompactResolvent
.........
74
7.4 TheGeneralCase .................
76
References
....................
77
8
A Weakly Singular Boundary Integral Formulation
of the External Helmholtz Problem Valid for All
Wavenumbers
Paul J. Harris, Ke Chen, and Jin Cheng
79
8.1 Introduction
...................
79
8.2
Boundary Integral Formulation
...........
79
8.3 NumericalMethods
................
81
8.4 NumericalResults .................
83
8.5 Conclusions ....................
86
References
....................
86
9
Cross-referencing for Determining Regularization
Parameters in Ill-Posed Imaging Problems
John W. Hilgers and Barbara S. Bertram
89
9.1 Introduction
...................
89
9.2 TheParameterChoiceProblem ...........
90
9.3 AdvantagesofCREF ................
91
9.4 Examples .....................
92
9.5 Summary .....................
95
References
....................
95
Contents
vii
10 A Numerical Integration Method for Oscillatory
Functions over an Infinite Interval by Substitution
and Taylor Series
Hiroshi Hirayama 99
10.1Introduction ................... 99
10.2TaylorSeries ................... 100
10.3 Integrals of Oscillatory Type ............ 101
10.4NumericalExamples ................ 103
10.5Conclusion .................... 104
References
.................... 104
11 On the Stability of Discrete Systems
Alexander O. Ignatyev and Oleksiy A. Ignatyev 105
11.1Introduction ................... 105
11.2MainDefinitionsandPre iminaries .......... 105
11.3 Stability of Periodic Systems ............ 107
11.4 Stability of Almost Periodic Systems
......... 110
References
.................... 115
12 Parallel Domain Decomposition Boundary Element
Method for Large-scale Heat Transfer Problems
AlainJ.KassabandEduardoA.Divo 117
12.1Introduction ................... 117
12.2App icationsinHeatTransfer ............ 118
12.3Exp icitDomainDecomposition ........... 125
12.4IterativeSolutionAlgorithm............. 127
12.5Para lelImplementationonaPCCluster ....... 130
12.6NumericalVa idationandExamples ......... 130
12.7Conclusions .................... 132
References
.................... 133
13 The Poisson Problem for the Lame System on
Low-dimensional Lipschitz Domains
Svitlana Mayboroda and Marius Mitrea 137
13.1IntroductionandStatementoftheMainResults .... 137
13.2EstimatesforSingularIntegralOperators ....... 141
13.3TracesandConormalDerivatives .......... 146
13.4 Boundary Integral Operators and Proofs of the Main
Results ...................... 152
13.5 Regularity of Green Potentials in Lipschitz Domains . . 153
13.6TheTwo-dimensionalSetting ............ 158
References
.................... 159
14 Analysis of Boundary-domain Integral and
Integro-differential Equations for a Dirichlet Problem
with a Variable Coe cient
Sergey E. Mikhailov 161
14.1Introduction ................... 161
14.2 Formulation of the Boundary Value Problem
..... 162

Plik z chomika:

Inne pliki z tego folderu:

Inne foldery tego chomika:

Zgłoś jeśli naruszono regulamin