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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 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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978-0-8176-4450-5 (9780817644505)
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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 theMonotone 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.
