Ebook: Integral Methods in Science and Engineering: Theoretical and Practical Aspects

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 the solution of these types of equations, which sometimes can be performed analytically, while at other times only numerically. This edited, self-contained volume presents a series of state-of-the-art analytic and numerical methods of solution constructed for important problems arising in science and engineering, all based on the powerful operation of (exact or approximate) integration.

The book, consisting of twenty seven selected chapters presented by well-known specialists in the field, is an outgrowth of the Eighth International Conference on Integral Methods in Science and Engineering, held August 2–4, 2004, in Orlando, FL. Contributors cover a wide variety of topics, from the theoretical development of boundary integral methods to the application of integration-based analytic and numerical techniques that include integral equations, finite and boundary elements, conservation laws, hybrid approaches, and other procedures.

The volume may be used as a reference guide and a practical resource. It is suitable for researchers and practitioners in applied mathematics, physics, and mechanical and electrical engineering, as well as graduate students in these disciplines.

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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 the solution of these types of equations, which sometimes can be performed analytically, while at other times only numerically. This edited, self-contained volume presents a series of state-of-the-art analytic and numerical methods of solution constructed for important problems arising in science and engineering, all based on the powerful operation of (exact or approximate) integration.

The book, consisting of twenty seven selected chapters presented by well-known specialists in the field, is an outgrowth of the Eighth International Conference on Integral Methods in Science and Engineering, held August 2–4, 2004, in Orlando, FL. Contributors cover a wide variety of topics, from the theoretical development of boundary integral methods to the application of integration-based analytic and numerical techniques that include integral equations, finite and boundary elements, conservation laws, hybrid approaches, and other procedures.

The volume may be used as a reference guide and a practical resource. It is suitable for researchers and practitioners in applied mathematics, physics, and mechanical and electrical engineering, as well as graduate students in these disciplines.

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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 the solution of these types of equations, which sometimes can be performed analytically, while at other times only numerically. This edited, self-contained volume presents a series of state-of-the-art analytic and numerical methods of solution constructed for important problems arising in science and engineering, all based on the powerful operation of (exact or approximate) integration.

The book, consisting of twenty seven selected chapters presented by well-known specialists in the field, is an outgrowth of the Eighth International Conference on Integral Methods in Science and Engineering, held August 2–4, 2004, in Orlando, FL. Contributors cover a wide variety of topics, from the theoretical development of boundary integral methods to the application of integration-based analytic and numerical techniques that include integral equations, finite and boundary elements, conservation laws, hybrid approaches, and other procedures.

The volume may be used as a reference guide and a practical resource. It is suitable for researchers and practitioners in applied mathematics, physics, and mechanical and electrical engineering, as well as graduate students in these disciplines.

Content:
Front Matter....Pages i-xvi
Newton-type Methods for Some Nonlinear Differential Problems....Pages 1-15
Nodal and Laplace Transform Methods for Solving 2D Heat Conduction....Pages 17-27
The Cauchy Problem in the Bending of Thermoelastic Plates....Pages 29-35
Mixed Initial-boundary Value Problems for Thermoelastic Plates....Pages 37-45
On the Structure of the Eigenfunctions of a Vibrating Plate with a Concentrated Mass and Very Small Thickness....Pages 47-59
A Finite-dimensional Stabilized Variational Method for Unbounded Operators....Pages 61-70
A Converse Result for the Tikhonov—Morozov Method....Pages 71-77
A Weakly Singular Boundary Integral Formulation of the External Helmholtz Problem Valid for All Wavenumbers....Pages 79-87
Cross-referencing for Determining Regularization Parameters in Ill-Posed Imaging Problems....Pages 89-98
A Numerical Integration Method for Oscillatory Functions over an Infinite Interval by Substitution and Taylor Series....Pages 99-104
On the Stability of Discrete Systems....Pages 105-116
Parallel Domain Decomposition Boundary Element Method for Large-scale Heat Transfer Problems....Pages 117-135
The Poisson Problem for the Lam? System on Low-dimensional Lipschitz Domains....Pages 137-160
Analysis of Boundary-domain Integral and Integro-differential Equations for a Dirichlet Problem with a Variable Coefficient....Pages 161-176
On the Regularity of the Harmonic Green Potential in Nonsmooth Domains....Pages 177-188
Applications of Wavelets and Kernel Methods in Inverse Problems....Pages 189-197
Zonal, Spectral Solutions for the Navier-Stokes Layer and Their Aerodynamical Applications....Pages 199-207
Hybrid Laplace and Poisson Solvers. Part III: Neumann BCs....Pages 209-217
Hybrid Laplace and Poisson Solvers. Part IV: Extensions....Pages 219-233
A Contact Problem for a Convection-diffusion Equation....Pages 235-244
Integral Representation of the Solution of Torsion of an Elliptic Beam with Microstructure....Pages 245-249
A Coupled Second-order Boundary Value Problem at Resonance....Pages 251-256
Multiple Impact Dynamics of a Falling Rod and Its Numerical Solution....Pages 257-269
On the Monotone Solutions of Some ODEs. I: Structure of the Solutions....Pages 271-277
On the Monotone Solutions of Some ODEs. II: Dead-core, Compact-support, and Blow-up Solutions....Pages 279-288
A Spectral Method for the Fast Solution of Boundary Integral Formulations of Elliptic Problems....Pages 289-297
The GILTT Pollutant Simulation in a Stable Atmosphere....Pages 299-308
Back Matter....Pages 309-312

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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 the solution of these types of equations, which sometimes can be performed analytically, while at other times only numerically. This edited, self-contained volume presents a series of state-of-the-art analytic and numerical methods of solution constructed for important problems arising in science and engineering, all based on the powerful operation of (exact or approximate) integration.

The book, consisting of twenty seven selected chapters presented by well-known specialists in the field, is an outgrowth of the Eighth International Conference on Integral Methods in Science and Engineering, held August 2–4, 2004, in Orlando, FL. Contributors cover a wide variety of topics, from the theoretical development of boundary integral methods to the application of integration-based analytic and numerical techniques that include integral equations, finite and boundary elements, conservation laws, hybrid approaches, and other procedures.

The volume may be used as a reference guide and a practical resource. It is suitable for researchers and practitioners in applied mathematics, physics, and mechanical and electrical engineering, as well as graduate students in these disciplines.

Content:
Front Matter....Pages i-xvi
Newton-type Methods for Some Nonlinear Differential Problems....Pages 1-15
Nodal and Laplace Transform Methods for Solving 2D Heat Conduction....Pages 17-27
The Cauchy Problem in the Bending of Thermoelastic Plates....Pages 29-35
Mixed Initial-boundary Value Problems for Thermoelastic Plates....Pages 37-45
On the Structure of the Eigenfunctions of a Vibrating Plate with a Concentrated Mass and Very Small Thickness....Pages 47-59
A Finite-dimensional Stabilized Variational Method for Unbounded Operators....Pages 61-70
A Converse Result for the Tikhonov—Morozov Method....Pages 71-77
A Weakly Singular Boundary Integral Formulation of the External Helmholtz Problem Valid for All Wavenumbers....Pages 79-87
Cross-referencing for Determining Regularization Parameters in Ill-Posed Imaging Problems....Pages 89-98
A Numerical Integration Method for Oscillatory Functions over an Infinite Interval by Substitution and Taylor Series....Pages 99-104
On the Stability of Discrete Systems....Pages 105-116
Parallel Domain Decomposition Boundary Element Method for Large-scale Heat Transfer Problems....Pages 117-135
The Poisson Problem for the Lam? System on Low-dimensional Lipschitz Domains....Pages 137-160
Analysis of Boundary-domain Integral and Integro-differential Equations for a Dirichlet Problem with a Variable Coefficient....Pages 161-176
On the Regularity of the Harmonic Green Potential in Nonsmooth Domains....Pages 177-188
Applications of Wavelets and Kernel Methods in Inverse Problems....Pages 189-197
Zonal, Spectral Solutions for the Navier-Stokes Layer and Their Aerodynamical Applications....Pages 199-207
Hybrid Laplace and Poisson Solvers. Part III: Neumann BCs....Pages 209-217
Hybrid Laplace and Poisson Solvers. Part IV: Extensions....Pages 219-233
A Contact Problem for a Convection-diffusion Equation....Pages 235-244
Integral Representation of the Solution of Torsion of an Elliptic Beam with Microstructure....Pages 245-249
A Coupled Second-order Boundary Value Problem at Resonance....Pages 251-256
Multiple Impact Dynamics of a Falling Rod and Its Numerical Solution....Pages 257-269
On the Monotone Solutions of Some ODEs. I: Structure of the Solutions....Pages 271-277
On the Monotone Solutions of Some ODEs. II: Dead-core, Compact-support, and Blow-up Solutions....Pages 279-288
A Spectral Method for the Fast Solution of Boundary Integral Formulations of Elliptic Problems....Pages 289-297
The GILTT Pollutant Simulation in a Stable Atmosphere....Pages 299-308
Back Matter....Pages 309-312
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