Integral Methods in Science and Engineering Theoretical and Practica
The quantitative and qualitative study of the physical world makes use of many mathematical models governed by a great diversity of ordinary, partial differential, integral, and integro-differential equations. An essential step in such investigations is t
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C. Constanda Z. Nashed D. Rollins Editors
Birkh¨auser 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), 1955QA431.I49 2005 2005053047 518 .66–dc22 ISBN-10: 0-8176-4377-X ISBN-13: 978-0-8176-4377-5
e-ISBN: 0-8176-4450-4
Printed on acid-free paper.
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(IBT)
Contents
Preface
xi
Contributors 1
2
3
4
xiii
Newton-type Methods for Some Nonlinear Differential Problems Mario Ahues and Alain Largillier 1.1 The General Framework . . . . . . . . . . . . . . 1.2 Nonlinear Boundary Value Problems . . . . . . . . . 1.3 Spectral Differential Problems . . . . . . . . . . . . 1.4 Newton Method for the Matrix Eigenvalue Problem . . References . . . . . . . . . . . . . . . . . . . .
1 1 6 9 13 14
Nodal and Laplace Transform Methods for Solving 2D Heat Conduction Ivanilda B. Aseka, Marco T. Vilhena, and Haroldo F. Campos Velho 2.1 Introduction . . . . . . . . . . . . . . . . . 2.2 Nodal Method in Multi-layer Heat Conduction . . 2.3 Numerical Results . . . . . . . . . . . . . . . 2.4 Final Remarks . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . .
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17 17 18 24 26 27
The Cauchy Problem in the Bending of Thermoelastic Plates Igor Chudinovich and Christian Constanda 3.1 Introduction . . . . . . . . . . . 3.2 Prer
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