Integral Methods in Science and Engineering / Edition 1

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Overview

This book is an outgrowth of the sixth international conference on integral methods in science and engineering. The chapters focus on the solution of mathematical models from various physical domains, using integral methods in conjunction with approximation schemes. Integral Methods in Science and Engineering describes the construction and application of various analytic and numerical integration techniques. Problem solving in areas such as solid mechanics, fluid dynamics, thermoelasticity, plates and shells, liquid crystals, diffusion and diffraction theory, Hamiltonian systems, resonance, nonlinear waves, plasma, flight dynamics, and structural networks are presented in an accessible manner. The book offers a vehicle for the quick dissemination of new results in these domains, and will help create an ideal environment for investigative interdisciplinary study among a variety of research areas.
Topics-
Offers an illustration by prominent researchers of efficient methods of solution with numerical results and rigorous analytic methods.
Presents applications of integral methods to a wide variety of mathematical and physical problems.
Provides new results in the study of various physical and mechanical models.
A clear, concise focus on a class of methodologies rather than a specific field of study. This book is a practical resource for a broad audience of professionals, researchers, and practitioners in applied mathematics, mechanical engineering, and theoretical physics, who are interested in current research in ordinary and partial differential equations, integral equations, numerical analysis, mechanics of solids, fluid mechanics, and mathematical physics.Graduate students will find this a helpful guide to the wide range of applications that integral methods have in science and engineering.
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Editorial Reviews

From the Publisher

"The present book…focuses on the solution of mathematical models from various physical domains, using integral methods in conjunction with approximation schemes. Actually, its aim is to show…research work in which integration, in one form or another, is the main investigative tool.

A lot of problems are solved in areas such as solid mechanics, fluid dynamics, thermoelasticity, plates and shells, liquid crystals, diffusion and diffraction theory, Hamiltonian systems, resonance, nonlinear waves, plasma, flight dynamics and structural networks.… Generally, this book provides new results in the study of various physical and mechanical models and offers illustrations of efficient methods with numerical results and analytical methods. It can be useful to researchers and practitioners in applied mathematics, mechanical engineering and theoretical physicists, interested in current research in ordinary and partial differential equations, integral equations and numerical analysis."

—Memoriile Sectiilor Stiintifice

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Product Details

  • ISBN-13: 9780817642136
  • Publisher: Birkhauser Verlag
  • Publication date: 10/26/2007
  • Edition description: 2002
  • Edition number: 1
  • Pages: 264
  • Product dimensions: 9.21 (w) x 6.14 (h) x 0.69 (d)

Table of Contents

Preface
Contributors
1 Use of Elastodynamic Reciprocity Theorems for Field Calculations 1
2 Linear Solvers for the Galerkin Boundary Element Method 15
3 Reciprocity of Hopf's and Feautrier's Operators in Radiation Transport Theory 21
4 Spectral Approximation of Weakly Singular Integrable Kernels Using Projections 27
5 Effect of Imperfect Interface on Thermal Inclusion with an Interior Radial Crack 33
6 An Integrodifferential Equation of Atomic Diffusion 39
7 Nonradiating Dislocations in Uniform Supersonic Motion in Anisotropic Linear Elastic Solids 45
8 On the Use of the Conjugate Gradient Method for the Numerical Solution of First-Kind Integral Equations in Two Variables 51
9 On the Stopping Criteria for Conjugate Gradient Solutions of First-Kind Integral Equations in Two Variables 57
10 An Initial-Boundary Value Problem for Thermoelastic Plates 63
11 A Global Existence Result for Functional Differential Equations with Causal Operators 69
12 Direct Stiffness-Modification Route to Linear Consistency Between Incompatible Finite Element Meshes 75
13 Nonlinear Dynamic Analysis of a Curved Beam Structure Using a Finite Element Method 81
14 Seminal Ideas in Integral Methods 87
15 Mixed Boundary Value Problem with Two Displacement Boundaries for Thin Plate Bending 99
16 Use of Cross-Referencing for Solving the Parameter Choice Problem in Generalized CLS 105
17 Numerical Technique for Solving an Ordinary Differential Equation by Picard's Method 111
18 On a Class of Boundary Conditions Splitting Coupled Thermoelasticity Problems 117
19 Recent Mathematical Developments for Functionally Graded Linearly Elastic Materials 123
20 Ground Vibration Dynamics During Pile Hammering 131
21 Connection Between Liquid Crystal Theory and Plate Theory 137
22 Product Integration Quadratures for the Radiative Transfer Problem with Hopf's Kernel 143
23 A Numerical Scheme for Determining Diffraction Coefficients in Anisotropic Materials 149
24 Effect of Imperfect Inclusion/Matrix Interaction Between a Circular Inclusion and a Radial Matrix Crack 155
25 Neutral Equations with Causal Operators 161
26 Computation of Free-Surface Flows Under the Influence of Pressure Distribution 167
27 Solution of Eigenvalue Problems for Rectangular Plates by Differential Transformation 173
28 Free Vibrations of Structural Hyperbolic Paraboloid Networks 179
29 Sharp Invertibility Results for Layer Potentials in 2D 185
30 An Enhanced Theory of Bending of Plates 191
31 Comparison of Zonal, Spectral Solutions for Compressible Boundary Layer and Navier-Stokes Equations 197
32 Hybrid Laplace and Poisson Solvers I: Dirichlet Boundary Conditions 203
33 Estimation of Boundary Conditions for Different Experimental Data Using the LTS[subscript N] Method and Tikhonov Regularization 209
34 Analytical-Numerical Treatment of the One-Phase Stefan Problem with Constant Applied Heat Flux 215
35 Integral Equations Arising in Boundary Value Problems at Resonance 221
36 Thermal Stress Analysis of an Elliptic Inclusion with Imperfect Interface Embedded in an Infinite Elastic Medium 227
37 Three-Dimensional Elasticity Solutions for Anisotropic and Inhomogeneous Plates and Shells 233
38 A Circular Inclusion with Homogeneous Interface 245
39 Multiwavelets for Geometrically Complicated Domains and Their Application to Boundary Element Methods 251
40 Mathematical Investigation of Contact Problems with Friction in Fracture Dynamics 257
Index 263
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