Read more
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 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.
List of contents
Preface
Contributors
Newton-type Methods for Some Nonlinear Differential Problems
Nodal and Laplace Transform Methods for Solving 2D Heat Conduction
The Cauchy Problem in the Bending of Thermoelastic Plates
Mixed Initial-boundary Value Problems for Thermoelastic Plates
On the Structure of the Eigenfunctions of a Vibrating Plate with a Concentrated Mass and Very Small Thickness
A Finite-dimensional Stabilized Variational Method for Unbounded Operators
A Converse Result for the Tikhonov Morozov Method
A Weakly Singular Boundary Integral Formulation of the External Helmholtz Problem Valid for All Wavenumbers
Cross-referencing for Determining Regularization Parameters in Ill-Posed Imaging Problems
A Numerical Integration Method for Oscillatory Functions over an Infinite Interval by Substitution and Taylor Series
On the Stability of Discrete Systems
Parallel Domain Decomposition Boundary Element Method for Large-scale Heat Transfer Problems
The Poisson Problem for the Lamé System on Low-dimensional Lipschitz Domains
Analysis of Boundary-domain Integral and Integro-differential Equations for a Dirichlet Problem with a Variable Coefficient
On the Regularity of the Harmonic Green Potential in Nonsmooth Domains
Applications of Wavelets and Kernel Methods in Inverse Problems
Zonal, Spectral Solutions for the Navier Stokes Layer and Their Aerodynamical Applications
Hybrid Laplace and Poisson Solvers. Part III: Neumann BCs
Hybrid Laplace and Poisson Solvers. Part IV: Extensions
A Contact Problem for a Convection-diffusion Equation
Integral Representation of the Solution of Torsion of an Elliptic Beam with Microstructure
A Coupled Second-order Boundary Value Problem at Resonance
Multiple Impact Dynamics of a Falling Rod and Its Numerical Solution
On the Monotone Solutions of Some ODEs. I: Structure of the Solutions
On the Monotone Solutions of Some ODEs. II: Dead-core, Compact-support, and Blow-up Solutions
A Spectral Method for the Fast Solution of Boundary Integral Formulations of Elliptic Problems
The GILTT Pollutant Simulation in a Stable Atmosphere
Index
Summary
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 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.
