Ebook: Integral Methods in Science and Engineering

"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

---

---

Content:
Front Matter....Pages i-xxii
Use of Elastodynamic Reciprocity Theorems for Field Calculations....Pages 1-14
Linear Solvers for the Galerkin Boundary Element Method....Pages 15-20
Reciprocity of Hopf’s and Feautrier’s Operators in Radiation Transport Theory....Pages 21-26
Spectral Approximation of Weakly Singular Integrable Kernels Using Projections....Pages 27-32
Effect of Imperfect Interface on a Thermal Inclusion with an Interior Radial Crack....Pages 33-38
An Integrodifferential Equation of Atomic Diffusion....Pages 39-44
Nonradiating Dislocations in Uniform Supersonic Motion in Anisotropic Linear Elastic Solids....Pages 45-50
On the Use of the Conjugate Gradient Method for the Numerical Solution of First-Kind Integral Equations in Two Variables....Pages 51-56
On the Stopping Criteria for Conjugate Gradient Solutions of First-Kind Integral Equations in Two Variables....Pages 57-62
An Initial-Boundary Value Problem for Thermoelastic Plates....Pages 63-68
A Global Existence Result for Functional Differential Equations with Causal Operators....Pages 69-74
Direct Stiffness-Modification Route to Linear Consistency Between Incompatible Finite Element Meshes....Pages 75-80
Nonlinear Dynamic Analysis of a Curved Beam Structure Using a Finite Element Method....Pages 81-86
Seminal Ideas in Integral Methods....Pages 87-97
Mixed Boundary Value Problem with Two Displacement Boundaries for Thin Plate Bending....Pages 99-104
Use of Cross-Referencing for Solving the Parameter Choice Problem in Generalized CLS....Pages 105-110
Numerical Technique for Solving an Ordinary Differential Equation by Picard’s Method....Pages 111-116
On a Class of Boundary Conditions Splitting Coupled Thermoelasticity Problems....Pages 117-122
Recent Mathematical Developments for Functionally Graded Linearly Elastic Materials....Pages 123-130
Ground Vibration Dynamics During Pile Hammering....Pages 131-136
Connection Between Liquid Crystal Theory and Plate Theory....Pages 137-142
Product Integration Quadratures for the Radiative Transfer Problem with Hopf’s Kernel....Pages 143-148
A Numerical Scheme for Determining Diffraction Coefficients in Anisotropic Materials....Pages 149-154
Effect of Imperfect Inclusion/Matrix Interaction Between a Circular Inclusion and a Radial Matrix Crack....Pages 155-160
Neutral Equations with Causal Operators....Pages 161-166
Computation of Free-Surface Flows Under the Influence of Pressure Distribution....Pages 167-172
Solution of Eigenvalue Problems for Rectangular Plates by Differential Transformation....Pages 173-178
Free Vibrations of Structural Hyperbolic Paraboloid Networks....Pages 179-184
Sharp Invertibility Results for Layer Potentials in 2D....Pages 185-190
An Enhanced Theory of Bending of Plates....Pages 191-196
Comparison of Zonal, Spectral Solutions for Compressible Boundary Layer and Navier—Stokes Equations....Pages 197-202
Hybrid Laplace and Poisson Solvers I: Dirichlet Boundary Conditions....Pages 203-208
Estimation of Boundary Conditions from Different Experimental Data Using the LTSN Method and Tikhonov Regularization....Pages 209-214
Analytical-Numerical Treatment of the One-Phase Stefan Problem with Constant Applied Heat Flux....Pages 215-220
Integral Equations Arising in Boundary Value Problems at Resonance....Pages 221-226
Thermal Stress Analysis of an Elliptic Inclusion with Imperfect Interface Embedded in an Infinite Elastic Medium....Pages 227-231
Three-Dimensional Elasticity Solutions for Anisotropic and Inhomogeneous Plates and Shells....Pages 233-244
A Circular Inclusion with Inhomogeneous Interface....Pages 245-250
Multiwavelets for Geometrically Complicated Domains and Their Application to Boundary Element Methods....Pages 251-256
Mathematical Investigation of Contact Problems with Friction in Fracture Dynamics....Pages 257-262
Back Matter....Pages 263-264

---

Content:
Front Matter....Pages i-xxii
Use of Elastodynamic Reciprocity Theorems for Field Calculations....Pages 1-14
Linear Solvers for the Galerkin Boundary Element Method....Pages 15-20
Reciprocity of Hopf’s and Feautrier’s Operators in Radiation Transport Theory....Pages 21-26
Spectral Approximation of Weakly Singular Integrable Kernels Using Projections....Pages 27-32
Effect of Imperfect Interface on a Thermal Inclusion with an Interior Radial Crack....Pages 33-38
An Integrodifferential Equation of Atomic Diffusion....Pages 39-44
Nonradiating Dislocations in Uniform Supersonic Motion in Anisotropic Linear Elastic Solids....Pages 45-50
On the Use of the Conjugate Gradient Method for the Numerical Solution of First-Kind Integral Equations in Two Variables....Pages 51-56
On the Stopping Criteria for Conjugate Gradient Solutions of First-Kind Integral Equations in Two Variables....Pages 57-62
An Initial-Boundary Value Problem for Thermoelastic Plates....Pages 63-68
A Global Existence Result for Functional Differential Equations with Causal Operators....Pages 69-74
Direct Stiffness-Modification Route to Linear Consistency Between Incompatible Finite Element Meshes....Pages 75-80
Nonlinear Dynamic Analysis of a Curved Beam Structure Using a Finite Element Method....Pages 81-86
Seminal Ideas in Integral Methods....Pages 87-97
Mixed Boundary Value Problem with Two Displacement Boundaries for Thin Plate Bending....Pages 99-104
Use of Cross-Referencing for Solving the Parameter Choice Problem in Generalized CLS....Pages 105-110
Numerical Technique for Solving an Ordinary Differential Equation by Picard’s Method....Pages 111-116
On a Class of Boundary Conditions Splitting Coupled Thermoelasticity Problems....Pages 117-122
Recent Mathematical Developments for Functionally Graded Linearly Elastic Materials....Pages 123-130
Ground Vibration Dynamics During Pile Hammering....Pages 131-136
Connection Between Liquid Crystal Theory and Plate Theory....Pages 137-142
Product Integration Quadratures for the Radiative Transfer Problem with Hopf’s Kernel....Pages 143-148
A Numerical Scheme for Determining Diffraction Coefficients in Anisotropic Materials....Pages 149-154
Effect of Imperfect Inclusion/Matrix Interaction Between a Circular Inclusion and a Radial Matrix Crack....Pages 155-160
Neutral Equations with Causal Operators....Pages 161-166
Computation of Free-Surface Flows Under the Influence of Pressure Distribution....Pages 167-172
Solution of Eigenvalue Problems for Rectangular Plates by Differential Transformation....Pages 173-178
Free Vibrations of Structural Hyperbolic Paraboloid Networks....Pages 179-184
Sharp Invertibility Results for Layer Potentials in 2D....Pages 185-190
An Enhanced Theory of Bending of Plates....Pages 191-196
Comparison of Zonal, Spectral Solutions for Compressible Boundary Layer and Navier—Stokes Equations....Pages 197-202
Hybrid Laplace and Poisson Solvers I: Dirichlet Boundary Conditions....Pages 203-208
Estimation of Boundary Conditions from Different Experimental Data Using the LTSN Method and Tikhonov Regularization....Pages 209-214
Analytical-Numerical Treatment of the One-Phase Stefan Problem with Constant Applied Heat Flux....Pages 215-220
Integral Equations Arising in Boundary Value Problems at Resonance....Pages 221-226
Thermal Stress Analysis of an Elliptic Inclusion with Imperfect Interface Embedded in an Infinite Elastic Medium....Pages 227-231
Three-Dimensional Elasticity Solutions for Anisotropic and Inhomogeneous Plates and Shells....Pages 233-244
A Circular Inclusion with Inhomogeneous Interface....Pages 245-250
Multiwavelets for Geometrically Complicated Domains and Their Application to Boundary Element Methods....Pages 251-256
Mathematical Investigation of Contact Problems with Friction in Fracture Dynamics....Pages 257-262
Back Matter....Pages 263-264
....