Integral Methods in Science and Engineering

This book will appeal to applied mathematicians, mechanical engineers, theoretical physicists, and graduate students researching in the areas of ordinary and partial differential equations, integral equations, numerical analysis, mechanics of solids, fluid mechanics and mathematical physics.

"The present bookfocuses on the solution of mathematical models from various physical domains, using integral methods in conjunction with approximation schemes. Actually, its aim is to showresearch 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

Klappentext

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.

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