Integral Methods in Science and Engineering, Volume 2 Computational Methods - Perez, Maria Eugenia; SpringerLink (Online service) (Boston, MA : Birkhäuser Boston : Imprint: Birkhäuser, 2010)
Mathematical models—including those based on ordinary, partial differential, integral, and integro-differential equations—are indispensable tools for studying the physical world and its natural manifestations. Because of the usefulness of these models, it is critical for practitioners to be able to find their solutions by analytic and/or computational means. This two-volume set is a collection of up-to-date research results that illustrate how a very important class of mathematical tools can be manipulated and applied to the study of real-life phenomena and processes occurring in specific problems of science and engineering. The two volumes contain 65 chapters, which are based on talks presented by reputable researchers in the field at the Tenth International Conference on Integral Methods in Science and Engineering. The chapters address a wide variety of methodologies, from the construction of boundary integral methods to the application of integration-based analytic and computational techniques in almost all aspects of today's technological world. Among the topics covered are deformable structures, traffic flow, acoustic wave propagation, spectral procedures, eutrophication of bodies of water, pollutant dispersion, spinal cord movement, submarine avalanches, and many others with an interdisciplinary flavor. Integral Methods in Science and Engineering, Volumes 1 and 2 are useful references for a broad audience of professionals, including pure and applied mathematicians, physicists, biologists, and mechanical, civil, and electrical engineers, as well as graduate students, who use integration as a fundamental technique in their research. Volume 1: ISBN 978-0-8176-4898-5 Volume 2: ISBN 978-0-8176-4896-1.
Error Bounds for Galerkin Approximations of Weakly Singular Integral Operators -- Construction of Solutions of the Hamburger#x2013;L#x00F6;wner Mixed Interpolation Problem for Nevanlinna Class Functions -- A Three-Dimensional Eutrophication Model: Analysis and Control -- An Analytical Solution for the Transient Two-Dimensional Advection#x2013;Diffusion Equation with Non-Fickian Closure in Cartesian Geometry by the Generalized Integral Transform Technique -- A Numerical Solution of the Dispersion Equation of Guided Wave Propagation in -Layered Media -- Discretization of Coefficient Control Problems with a Nonlinear Cost in the Gradient -- Optimal Control and Vanishing Viscosity for the Burgers Equation -- A High-Order Finite Volume Method for Nonconservative Problems and Its Application to Model Submarine Avalanches -- Convolution Quadrature Galerkin Method for the Exterior Neumann Problem of the Wave Equation -- Solution Estimates in Classical Bending of Plates -- Modified Newton#x2019;s Methods for Systems of Nonlinear Equations -- Classification of Some Penalty Methods -- A Closed-Form Formulation for Pollutant Dispersion in the Atmosphere -- High-Order Methods for Weakly Singular Volterra Integro-Differential Equations -- Numerical Solution of a Class of Integral Equations Arising in a Biological Laboratory Procedure -- A Mixed Two-Grid Method Applied to a Fredholm Equation of the Second Kind -- Homogenized Models of Radiation Transfer in Multiphase Media -- A Porous Finite Element Model of the Motion of the Spinal Cord -- Boundary Hybrid Galerkin Method for Elliptic and Wave Propagation Problems in #x211D; over Planar Structures -- Boundary Integral Solution of the Time-Fractional Diffusion Equation -- Boundary Element Collocation Method for Time-Fractional Diffusion Equations -- Wavelet-Based H#x00F6;lder Regularity Analysis in Condition Monitoring -- Integral Equation Technique for Finding the Current Distribution of Strip Antennas in a Gyrotropic Medium -- A Two-Grid Method for a Second Kind Integral Equation with Green#x2019;s Kernel -- A Brief Overview of Plate Finite Element Methods -- Influence of a Weak Aerodynamics/Structure Interaction on the Aerodynamical Global Optimization of Shape -- Multiscale Investigation of Solutions of the Wave Equation -- The Laplace Transform Method for the Albedo Boundary Conditions in Neutron Diffusion Eigenvalue Problems -- Solution of the Fokker#x2013;Planck Pencil Beam Equation for Electrons by the Laplace Transform Technique -- Nonlinear Functional Parabolic Equations -- Grid Computing for Multi-Spectral Tomographic Reconstruction of Chlorophyll Concentration in Ocean Water -- Long-Time Solution of the Wave Equation Using Nonlinear Dissipative Structures -- High-Performance Computing for Spectral Approximations -- An Analytical Solution for the General Perturbed Diffusion Equation by an Integral Transform Technique.
Keywords: Integral equations; Applied mathematics; Engineering mathematics; Differential equations; Partial differential equations; Mechanical engineering; Physics; Integral Equations; Mathematical and Computational Engineering; Ordinary Differential Equations; Partial Differential Equations; Mechanical Engineering; Mathematical Methods in Physics