الصفحة 1
الصفحة 1
The Functional Calculus for Sectorial Operators
The present monograph deals with the functional calculus for unbounded operators in general and for sectorial operators in particular. Sectorial operators abound in the theory of evolution equations, especially those of parabolic type. They satisfy a certain resolvent condition that leads to a holomorphic functional calculus based on Cauchy-type integrals. Via an abstract extension procedure, this elementary functional calculus is then extended to a large class of (even meromorphic) functions. With this functional calculus at hand, the book elegantly covers holomorphic semigroups, fractional powers, and logarithms. Special attention is given to perturbation results and the connection with the theory of interpolation spaces. A chapter is devoted to the exciting interplay between numerical range conditions, similarity problems and functional calculus on Hilbert spaces. Two chapters describe applications, for example to elliptic operators, to numerical approximations of parabolic equations, and to the maximal regularity problem. This book is the first systematic account of a subject matter which lies in the intersection of operator theory, evolution equations, and harmonic analysis.
The Fast Solution of Boundary Integral Equations
The use of surface potentials to describe solutions of partial differential equations goes back to the middle of the 19th century. Numerical approximation procedures, known today as Boundary Element Methods (BEM), have been developed in the physics and engineering community since the 1950s. These methods turn out to be powerful tools for numerical studies of various physical phenomena which can be described mathematically by partial differential equations. The Fast Solution of Boundary Integral Equations provides a detailed description of fast boundary element methods which are based on rigorous mathematical analysis. In particular, a symmetric formulation of boundary integral equations is used, Galerkin discretisation is discussed, and the necessary related stability and error estimates are derived. For the practical use of boundary integral methods, efficient algorithms together with their implementation are needed.
Numerical Methods for Controlled Stochastic Delay Systems
The Markov chain approximation methods are widely used for the numerical solution of nonlinear stochastic control problems in continuous time. This book extends the methods to stochastic systems with delays. Because such problems are infinite-dimensional, many new issues arise in getting good numerical approximations and in the convergence proofs. Useful forms of numerical algorithms and system approximations are developed in this work, and the convergence proofs are given. All of the usual cost functions are treated as well as singular and impulsive controls. A major concern is on representations and approximations that use minimal memory.
Numerical Approximation Methods for Elliptic Boundary Value Problems : Finite and Boundary Elements
Although the aim of this book is to give a unified introduction into finite and boundary element methods, the main focus is on the numerical analysis of boundary integral and boundary element methods. Starting from the variational formulation of elliptic boundary value problems boundary integral operators and associated boundary integral equations are introduced and analyzed. By using finite and boundary elements corresponding numerical approximation schemes are considered.
Numerical Analysis and Its Applications ; 3rd International Conference, NAA 2004, Rousse, Bulgaria, June 29 - July 3, 2004, Revised Selected Papers
Constitutes the refereed post-proceedings of the Third International Conference on Numerical Analysis and Its Applications, held in Bulgaria in June/July 2004. This book addresses various aspects of numerical analysis. It covers the application fields such as computational sciences and engineering, chemistry, physics, economics, and simulation.
Numerical analysis
Introduces readers to the theory and application of modern numerical approximation techniques. Providing an accessible treatment that only requires a calculus prerequisite, the authors explain how, why, and when approximation techniques can be expected to work-and why, in some situations, they fail. A wealth of examples and exercises develop readers' intuition, and demonstrate the subject's practical applications to important everyday problems in math, computing, engineering, and physical science disciplines.
High Energy Polarized Proton Beams : A Modern View
This monograph begins with a review of the basic equations of spin motion in particle accelerators. It then reviews how polarized protons can be accelerated to several tens of GeV using as examples the preaccelerators of HERA, a 6.3 km long cyclic accelerator at DESY / Hamburg. Such techniques have already been used at the AGS of BNL / New York, to accelerate polarized protons to 25 GeV. But for acceleration to energies of several hundred GeV as in RHIC, TEVATRON, HERA, LHC, or a VLHC, new problems can occur which can lead to a significantly diminished beam polarization. For these high energies, it is necessary to look in more detail at the spin motion, and for that the invariant spin field has proved to be a useful tool. This is already widely used for the description of high-energy electron beams that become polarized by the emission of spin-flip synchrotron radiation. It is shown that this field gives rise to an adiabatic invariant of spin-orbit motion and that it defines the maximum time average polarization available to a particle physics experiment.
Digital Simulation in Electrochemistry
The book shows how to numerically solve the parabolic partial differential equations (pdes) encountered in electroanalytical chemistry. It does this in a didactic manner, by first introducing the basic equations to be solved and some model systems as text cases, for which solutions exist. Then it treats basic numerical approximation for derivatives and techniques for the numerical solution of ordinary differential equations, from which the more complicated methods for pdes can be derived. The major implicit methods are described in detail, and the handling of homogeneous chemical reactions, including coupled and nonlinear cases, is detailed. More advanced techniques are presented briefly, as well as some commercially available program packages.
Analysis and Numerics for Conservation Laws
The physical and chemical mechanisms as well as the sizes of these processes are quite different. So are the motivations for studying them scientifically.The super- 8 nova is a thermo-nuclear explosion on a scale of 10 cm. Astrophysicists try to understand them in order to get insight into fundamental properties of the universe. In hows around airfoils of commercial airliners at the scale of 3 10 cm shock waves occur that influence the stability of the wings as well as fuel consumption in ight. This requires appropriate design of the shape and structure of airfoils by engineers. Knocking occurs in combustion, a chemical 1 process, and must be avoided since it damages motors. The scale is 10 cm and these processes must be optimized for efficiency and environmental conside- tions. The common thread is that the underlying ?uid ?ows may at a certain scale of observation be described by basically the same type of hyperbolic s- tems of partial differential equations in divergence form, called conservation laws. Astrophysicists, engineers and mathematicians share a common interest in scientific progress on theory for these equations and the development of computational methods for solutions of the equations. Due to their wide applicability in modeling of continua. A substantial portion of mathematical research is related to the analysis and numerical approximation of solutions to such equations. Hyperbolic conservation laws in two or more space dimensions still poseone of the main challenges to modern mathematics.
A Posteriori Error Analysis Via Duality Theory : With Applications in Modeling and Numerical Approximations
This volume provides a posteriori error analysis for mathematical idealizations in modeling boundary value problems, especially those arising in mechanical applications, and for numerical approximations of numerous nonlinear variational problems. The author avoids giving the results in the most general, abstract form so that it is easier for the reader to understand more clearly the essential ideas involved. Many examples are included to show the usefulness of the derived error estimates.
