الصفحة 1
الصفحة 1
Singular Perturbation Theory : Mathematical and Analytical Techniques with Applications to Engineering
Singular Perturbation Theory introduces all the background ideas to this subject, designed for those with only the most superficial familiarity with university-level mathematics. The methods are developed through worked examples and set exercises (with answers); the latter part of the book is devoted to applications drawn from: mechanics, physics, semi- and superconductor theory, fluid mechanics, thermal processes, chemical and biochemical reactions. In a novel approach, these are grouped together so that the reader with particular interests can readily access them.
Robust Numerical Methods for Singularly Perturbed Differential Equations : Convection-Diffusion-Reaction and Flow Problems
This considerably extended and completely revised second edition incorporates many new developments in the thriving field of numerical methods for singularly perturbed differential equations. It provides a thorough foundation for the numerical analysis and solution of these problems, which model many physical phenomena whose solutions exhibit layers. The book focuses on linear convection-diffusion equations and on nonlinear flow problems that appear in computational fluid dynamics. It offers a comprehensive overview of suitable numerical methods while emphasizing those with realistic error estimates. The book should be useful for scientists requiring effective numerical methods for singularly perturbed differential equations.
Proceedings of the Conference on Applied Mathematics and Scientific Computing
Brings together papers presenting results covering areas of applied mathematics and scientific computing. This work offers presentations in the fields of numerical linear algebra, shape preserving approximation and singular perturbation theory. It includes an overview of numerical solutions to skew-Hamiltonian and Hamiltonian eigenvalue problems.
Numerical Mathematics and Advanced Applications ; Proceedings of ENUMATH 2005 the 6th European Conference on Numerical Mathematics and Advanced Applications, Santiago de Compostela, Spain, July 2005
This book include applications such as atmosphere and ocean, water pollution, electromagnetism, interface problems, waves, finance, heat transfer, unbounded domains, numerical linear algebra, convection-diffusion, fluid-structure, plates, solids, hyperbolic equations, multiphase flow, Navier-Stokes, singular perturbation problems, non linear PDE, control, parabolic equations, as well as methodologies such as a posteriori error estimates, discontinuous Galerkin methods, multiscale methods, optimization, adaptive methods, domain decomposition techniques, exponential integrators, hp-finite elements, level set methods, fractional step methods, penalty procedures, and finite volumes. The book gives an extensive overview of the most recent research in scientific computing, providing to the reader the latest developments concerning the mathematical issues and the applications of this active field of science.
Noise-Induced Phenomena in Slow-Fast Dynamical Systems : A Sample-Paths Approach
Stochastic differential equations play an increasingly important role in modeling the dynamics of a large variety of systems in the natural sciences, and in technological applications. This book presents a new constructive approach to the quantitative description of solutions to systems of stochastic differential equations evolving on well-separated timescales. The method, which combines techniques from stochastic analysis and singular perturbation theory, allows the domains of concentration for typical sample paths to be determined, and provides precise estimates on the transition probabilities between these domains. In addition to the detailed presentation of the set-up and mathematical results, applications to problems in physics, biology, and climatology are discussed. The emphasis lies on noise-induced phenomena such as stochastic resonance, hysteresis, excitability, and the reduction of bifurcation delay.
Methods and Applications of Singular Perturbations : Boundary Layers and Multiple Timescale Dynamics
Perturbation theory, one of the most intriguing and essential topics in mathematics, and its applications to the natural and engineering sciences.In a systematic introductory manner, this unique book deliniates boundary layer theory for ordinary and partial differential equations, multi-timescale phenomena for nonlinear oscillations, diffusion and nonlinear wave equations. The book provides analysis of simple examples in the context of the general theory, as well as a final discussion of the more advanced problems.
Asymptotic Analysis and Boundary Layers
Presents a new method of asymptotic analysis of boundary-layer problems, the Successive Complementary Expansion Method (SCEM). The first part is devoted to a general comprehensive presentation of the tools of asymptotic analysis. It gives the keys to understand a boundary-layer problem and explains the methods to construct an approximation. The second part is devoted to SCEM and its applications in fluid mechanics, including external and internal flows. The advantages of SCEM are discussed in comparison with the standard Method of Matched Asymptotic Expansions. In particular, for the first time, the theory of Interactive Boundary Layer is fully justified. With its chapter summaries, detailed derivations of results, discussed examples and fully worked out problems and solutions, the book is self-contained.
