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Integral Methods in Science and Engineering: Computational and Analytic Aspects

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The systematic study of the physical world is largely based on the design of mathematical models using many different types of ordinary differential, partial differential, integral, and integro-differential equations. The solutions of these equations are therefore of great interest to practitioners and to science in general. With a wealth of cutting-edge research in the field, Integral Methods in Science and Engineering: Computational and Analytic Aspects provides a vivid picture of both the development of theoretical integral techniques and their use in specific science and engineering problems.

The volume is an outgrowth of talks presented by world-renowned researchers at the Eleventh International Conference on Integral Methods in Science and Engineering held in Brighton, UK, July 12–14, 2010. The array of topics they address is immense, ranging from theoretical advances in boundary integral methods to applications of analytic and numerical quadrature techniques as diverse as integral equations, finite and boundary elements, conservation laws, hybrid approaches, and more.

With ample coverage of theory and applications, this book will be a valuable resource for researchers in applied mathematics, physics, and mechanical and electrical engineering, for graduate students in these disciplines, and for various other professionals who use integration as an essential technique in their work.

Author(s): M. Ahues, A. Mennouni (auth.), Christian Constanda, Paul J. Harris (eds.)
Edition: 1
Publisher: Birkhäuser Basel
Year: 2011

Language: English
Pages: 422
Tags: Integral Equations; Appl.Mathematics/Computational Methods of Engineering; Ordinary Differential Equations; Partial Differential Equations; Continuum Mechanics and Mechanics of Materials; Computational Mathematics and Numerical Analysis

Front Matter....Pages I-XXV
A Collocation Method for Cauchy Integral Equations in L 2 ....Pages 1-5
On a New Definition of the Reynolds Number from the Interplay of Macroscopic and Microscopic Phenomenology....Pages 7-14
A Self-Consistent Monte Carlo Validation Procedure for Hadron Cancer Therapy Simulation....Pages 15-23
A General Analytical Solution of the Advection–Diffusion Equation for Fickian Closure....Pages 25-34
A Novel Method for Simulating Spectral Nuclear Reactor Criticality by a Spatially Dependent Volume Size Control....Pages 35-45
Adaptive Particle Filter for Stable Distribution....Pages 47-57
On the Analytical Solution of the Multi-Group Neutron Diffusion Kinetic Equation in One-Dimensional Cartesian Geometry by an Integral Transform Technique....Pages 59-67
Estimating the Validity of Statistical Energy Analysis Using Dynamical Energy Analysis: A Preliminary Study....Pages 69-78
Efficient Iterative Methods for Fast Solution of Integral Operators Related Problems....Pages 79-90
Analysis of Some Localized Boundary–Domain Integral Equations for Transmission Problems with Variable Coefficients....Pages 91-108
Analysis of Segregated Boundary–Domain Integral Equations for Mixed Variable-Coefficient BVPs in Exterior Domains....Pages 109-128
Thermoelastic Plates with Arc-Shaped Cracks....Pages 129-140
Almost Periodicity in Semilinear Systems....Pages 141-146
Bubble Behavior Near a Two Fluid Interface....Pages 147-158
Spectral Stiff Problems in Domains with a Strongly Oscillating Boundary....Pages 159-172
Spectra and Pseudospectra of a Convection–Diffusion Operator....Pages 173-180
A Necessary and Sufficient Condition for the Existence of Absolute Minimizers for Energy Functionals with Scale Invariance....Pages 181-190
Nonlinear Abel-Type Integral Equation in Modeling Creep Crack Propagation....Pages 191-201
Some Thoughts on Methods for Evaluating a Class of Highly Oscillatory Integrals....Pages 203-211
Numerical Experiments for Mammary Adenocarcinoma Cell Progression....Pages 213-224
Limiting Cases of Subdiffusion....Pages 225-231
A New Hybrid Method to Predict the Distribution of Vibro-Acoustic Energy in Complex Built-Up Structures....Pages 233-240
2-D and 3-D Elastodynamic Contact Problems for Interface Cracks Under Harmonic Loading....Pages 241-252
Asymptotic Behavior of Elliptic Quadratic Algebraic Equations with Variable Coefficients, and Aerodynamical Applications....Pages 253-260
Artificial Neural Networks for Estimating the Atmospheric Pollutant Sources....Pages 261-271
A Theoretical Study of the Stratified Atmospheric Boundary Layer Through Perturbation Techniques....Pages 273-286
Integro-Differential Equations for Stress Analysis in the Bridged Zone of Interface Cracks....Pages 287-298
Design and Performance of Gas–Liquid Cylindrical Cyclone/Slug Damper System....Pages 299-311
On Quasimodes for Compact Operators and Associated Evolution Problems....Pages 313-325
Error Estimation by Means of Richardson Extrapolation with the Boundary Element Method in a Dirichlet Problem for the Laplace Equation....Pages 327-338
Convergence of a Discretization Scheme Based on the Characteristics Method for a Fluid–Rigid System....Pages 339-348
An Efficient Algorithm to Solve the GITT-Transformed 2-D Neutron Diffusion Equation....Pages 349-355
Nonlinear Localized Dissipative Structures for Solving Wave Equations over Long Distances....Pages 357-368
Semianalytical Approach to the Computation of the Laplace Transform of Source Functions....Pages 369-378
Asymptotic Analysis of Singularities for Pseudodifferential Equations in Canonical Non-Smooth Domains....Pages 379-389
Optimizing Water Quality in a River Section....Pages 391-402
Boundary Integral Equations for Arbitrary Geometry Shells....Pages 403-414
Back Matter....Pages 415-419