Numerical Methods that Work

Author: Forman S. Acton

Publisher: MAA

ISBN: 9780883854501

Category: Mathematics

Page: 549

View: 6371

A commonsense approach to numerical algorithms for the solution of equations.

Numerical Analysis for Electromagnetic Integral Equations

Author: Karl F. Warnick

Publisher: Artech House

ISBN: 1596933348

Category: Electrical engineering

Page: 233

View: 7917

This unique volume is the first book on integral equation-based methods that combines quantitative formulas for predicting numerical simulation accuracy together with rigorous error estimates and results for dozens of actual electromagnetics and wave propagation problems. You get the latest insights on accuracy-improving methods like regularization and error-increasing effects such as edge singularities and resonance, along with full details on how to determine mesh density, choice of basis functions, and other parameters needed to optimize any numerical simulation.

Numerical Analysis of Spectral Methods

Theory and Applications

Author: David Gottlieb,Steven A. Orszag

Publisher: SIAM

ISBN: 9781611970425

Category: Differential equations

Page: 161

View: 7083

A unified discussion of the formulation and analysis of special methods of mixed initial boundary-value problems. The focus is on the development of a new mathematical theory that explains why and how well spectral methods work. Included are interesting extensions of the classical numerical analysis.

Numerical Methods in Fluid Mechanics

Author: Alain Vincent

Publisher: American Mathematical Soc.

ISBN: 9780821808139

Category: Science

Page: 199

View: 9358

After centuries of research, turbulence in fluids is still an unsolved problem. The graduate-level lectures in this volume cover the state of the art of numerical methods for fluid mechanics. The research in this collection covers wavelet-based methods, the semi-Lagrangian method, the Lagrangian multi-pole method, continuous adaptation of curvilinear grids, finite volume methods, shock-capturing methods, and ENO schemes. The most recent research on large eddy simulations and Reynolds stress modeling is presented in a way that is accessible to engineers, postdoctoral researchers, and graduate students. Applications cover industrial flows, aerodynamics, two-phase flows, astrophysical flows, and meteorology. This volume would be suitable as a textbook for graduate students with a background in fluid mechanics.

Numerical Methods for Solving Partial Differential Equations

A Comprehensive Introduction for Scientists and Engineers

Author: George F. Pinder

Publisher: John Wiley & Sons

ISBN: 1119316111

Category: Mathematics

Page: 320

View: 9444

A comprehensive guide to numerical methods for simulating physical-chemical systems This book offers a systematic, highly accessible presentation of numerical methods used to simulate the behavior of physical-chemical systems. Unlike most books on the subject, it focuses on methodology rather than specific applications. Written for students and professionals across an array of scientific and engineering disciplines and with varying levels of experience with applied mathematics, it provides comprehensive descriptions of numerical methods without requiring an advanced mathematical background. Based on its author’s more than forty years of experience teaching numerical methods to engineering students, Numerical Methods for Solving Partial Differential Equations presents the fundamentals of all of the commonly used numerical methods for solving differential equations at a level appropriate for advanced undergraduates and first-year graduate students in science and engineering. Throughout, elementary examples show how numerical methods are used to solve generic versions of equations that arise in many scientific and engineering disciplines. In writing it, the author took pains to ensure that no assumptions were made about the background discipline of the reader. Covers the spectrum of numerical methods that are used to simulate the behavior of physical-chemical systems that occur in science and engineering Written by a professor of engineering with more than forty years of experience teaching numerical methods to engineers Requires only elementary knowledge of differential equations and matrix algebra to master the material Designed to teach students to understand, appreciate and apply the basic mathematics and equations on which Mathcad and similar commercial software packages are based Comprehensive yet accessible to readers with limited mathematical knowledge, Numerical Methods for Solving Partial Differential Equations is an excellent text for advanced undergraduates and first-year graduate students in the sciences and engineering. It is also a valuable working reference for professionals in engineering, physics, chemistry, computer science, and applied mathematics.

A Bayesian Analysis of QCD Sum Rules

Author: Philipp Gubler

Publisher: Springer Science & Business Media

ISBN: 443154318X

Category: Science

Page: 190

View: 1305

The author develops a novel analysis method for QCD sum rules (QCDSR) by applying the maximum entropy method (MEM) to arrive at an analysis with less artificial assumptions than previously held. This is a first-time accomplishment in the field. In this thesis, a reformed MEM for QCDSR is formalized and is applied to the sum rules of several channels: the light-quark meson in the vector channel, the light-quark baryon channel with spin and isospin 1/2, and several quarkonium channels at both zero and finite temperatures. This novel technique of combining QCDSR with MEM is applied to the study of quarkonium in hot matter, which is an important probe of the quark-gluon plasma currently being created in heavy-ion collision experiments at RHIC and LHC.

Handbook of Numerical Analysis

Solution of Equations in Rn (Part 4), Techniques of Scientific Computer (Part 4), Numerical Methods for Fluids

Author: Philippe G. Ciarlet,Jacques-Louis Lions

Publisher: Gulf Professional Publishing

ISBN: 9780444509062

Category: Mathematics

Page: 650

View: 8637

This series of volumes covers all the major aspects of numerical analysis, serving as the basic reference work on the subject. Each volume concentrates on one to three particular topics. Each article, written by an expert, is an in-depth survey, reflecting up-to-date trends in the field, and is essentially self-contained. The handbook will cover the basic methods of numerical analysis, under the following general headings: solution of equations in Rn; finite difference methods; finite element methods; techniques of scientific computing; optimization theory; and systems science. It will also cover the numerical solution of actual problems of contemporary interest in applied mathematics, under the following headings: numerical methods for fluids; numerical methods for solids; and specific applications - including meteorology, seismology, petroleum mechanics and celestial mechanics.

Spectral Methods for Non-Standard Eigenvalue Problems

Fluid and Structural Mechanics and Beyond

Author: Călin-Ioan Gheorghiu

Publisher: Springer Science & Business

ISBN: 3319062301

Category: Mathematics

Page: 120

View: 9731

This book focuses on the constructive and practical aspects of spectral methods. It rigorously examines the most important qualities as well as drawbacks of spectral methods in the context of numerical methods devoted to solve non-standard eigenvalue problems. In addition, the book also considers some nonlinear singularly perturbed boundary value problems along with eigenproblems obtained by their linearization around constant solutions. The book is mathematical, poising problems in their proper function spaces, but its emphasis is on algorithms and practical difficulties. The range of applications is quite large. High order eigenvalue problems are frequently beset with numerical ill conditioning problems. The book describes a wide variety of successful modifications to standard algorithms that greatly mitigate these problems. In addition, the book makes heavy use of the concept of pseudospectrum, which is highly relevant to understanding when disaster is imminent in solving eigenvalue problems. It also envisions two classes of applications, the stability of some elastic structures and the hydrodynamic stability of some parallel shear flows. This book is an ideal reference text for professionals (researchers) in applied mathematics, computational physics and engineering. It will be very useful to numerically sophisticated engineers, physicists and chemists. The book can also be used as a textbook in review courses such as numerical analysis, computational methods in various engineering branches or physics and computational methods in analysis.

Applied Many-Body Methods in Spectroscopy and Electronic Structure

Author: D. Mukherjee

Publisher: Springer Science & Business Media

ISBN: 1475792565

Category: Science

Page: 291

View: 2369

There has been a steady advance of the atomic and molecular many-body methodology over the last few years, with a concomitant development of versatile computer codes. Understanding and interpretation of electronic structural features and the associated spectroscopic properties via many-body techniques are becoming competitive with those obtained with the traditional formalisms. Since the many-body techniques are not yet a part of the repertoire of the "black-box tools" of electronic structure and spectroscopy, it seems worthwhile to take stock now of the recent progress in certain selected areas. The present volume is more in the nature of proceedings of a "Paper Symposium," rather than of one which actually took place. We did organize in Calcutta, between December 10 and 12, 1990, a small meeting on Applied Many-Body Methods to Spectroscopy and Electronic Structure, jointly organized by the Indian Association for the Cultivation of Science and the S.N. Bose National Centre for Basic Sciences. Several leading practitioners were invited, among which some could not come for various reasons.

Numerical Analysis

A.R. Mitchell 75th Birthday Volume

Author: Andrew R. Mitchell,David Francis Griffiths,G. A. Watson

Publisher: World Scientific

ISBN: 9789810227197

Category: Nature

Page: 370

View: 5409

This volume is intended to mark the 75th birthday of A R Mitchell, of the University of Dundee. It consists of a collection of articles written by numerical analysts having links with Ron Mitchell, as colleagues, collaborators, former students, or as visitors to Dundee. Ron Mitchell is known for his books and articles contributing to the numerical analysis of partial differential equations; he has also made major contributions to the development of numerical analysis in the UK and abroad, and his many human qualitites are such that he is held in high regard and looked on with great affection by the numerical analysis community. The list of contributors is evidence of the esteem in which he is held, and of the way in which his influence has spread through his former students and fellow workers. In addition to contributions relevant to his own specialist subjects, there are also papers on a wide range of subjects in numerical analysis.

Numerical Analysis of Partial Differential Equations

Lectures given at a Summer School of the Centro Internazionale Matematico Estivo (C.I.M.E.) held in Ispra (Varese), Italy, July 3-11, 1967

Author: Jacques Louis Lions

Publisher: Springer Science & Business Media

ISBN: 9783642110573

Category: Mathematics

Page: 468

View: 1647

S. Albertoni: Alcuni metodi di calcolo nella teoria della diffusione dei neutroni.- I. Babuska: Optimization and numerical stability in computations.- J.H. Bramble: Error estimates in elliptic boundary value problems.- G. Capriz: The numerical approach to hydrodynamic problems.- A. Dou: Energy inequalities in an elastic cylinder.- T. Doupont: On the existence of an iterative method for the solution of elliptic difference equation with an improved work estimate.- J. Douglas, J.R. Cannon: The approximation of harmonic and parabolic functions of half-spaces from interior data.- B.E. Hubbard: Error estimates in the fixed Membrane problem.- K. Jorgens: Calculation of the spectrum of a Schrödinger operator.- A. Lasota: Contingent equations and boundary value problems.- J.L. Lions: Réduction à des problèmes du type Cauchy-Kowalewska.- J.L. Lions: Problèmes aux limites non homogènes à données irrégulières; une méthode d’approximation.- J.L. Lions: Remarques sur l’approximation régularisée de problèmes aux limites.- W.V. Petryshyn: On the approximation-solvability of nonlinear functional equations in normed linear spaces.- P.A. Raviart: Approximation des équations d’évolution par des méthodes variationnelles.- M. Sibony, H. Brezis: Méthodes d’approximation et d’itération pour les operateurs monotones.- V. Thomee: Some topics in stability theory for partial difference operators.

SIAM Journal on Numerical Analysis

A Publication of the Society of Industrial and Applied Mathematics

Author: N.A

Publisher: N.A

ISBN: N.A

Category: Numerical analysis

Page: N.A

View: 2990

A Theoretical Introduction to Numerical Analysis

Author: Victor S. Ryaben'kii,Semyon V. Tsynkov

Publisher: CRC Press

ISBN: 9781584886075

Category: Mathematics

Page: 552

View: 6305

A Theoretical Introduction to Numerical Analysis presents the general methodology and principles of numerical analysis, illustrating these concepts using numerical methods from real analysis, linear algebra, and differential equations. The book focuses on how to efficiently represent mathematical models for computer-based study. An accessible yet rigorous mathematical introduction, this book provides a pedagogical account of the fundamentals of numerical analysis. The authors thoroughly explain basic concepts, such as discretization, error, efficiency, complexity, numerical stability, consistency, and convergence. The text also addresses more complex topics like intrinsic error limits and the effect of smoothness on the accuracy of approximation in the context of Chebyshev interpolation, Gaussian quadratures, and spectral methods for differential equations. Another advanced subject discussed, the method of difference potentials, employs discrete analogues of Calderon’s potentials and boundary projection operators. The authors often delineate various techniques through exercises that require further theoretical study or computer implementation. By lucidly presenting the central mathematical concepts of numerical methods, A Theoretical Introduction to Numerical Analysis provides a foundational link to more specialized computational work in fluid dynamics, acoustics, and electromagnetism.

Thermal Radiation Heat Transfer, Fourth Edition

Author: Robert Siegel

Publisher: CRC Press

ISBN: 9781560328391

Category: Technology & Engineering

Page: 864

View: 8376

This extensively revised 4th edition provides an up-to-date, comprehensive single source of information on the important subjects in engineering radiative heat transfer. It presents the subject in a progressive manner that is excellent for classroom use or self-study, and also provides an annotated reference to literature and research in the field. The foundations and methods for treating radiative heat transfer are developed in detail, and the methods are demonstrated and clarified by solving example problems. The examples are especially helpful for self-study. The treatment of spectral band properties of gases has been made current and the methods are described in detail and illustrated with examples. The combination of radiation with conduction and/or convection has been given more emphasis nad has been merged with results for radiation alone that serve as a limiting case; this increases practicality for energy transfer in translucent solids and fluids. A comprehensive catalog of configuration factors on the CD that is included with each book provides over 290 factors in algebraic or graphical form. Homework problems with answers are given in each chapter, and a detailed and carefully worked solution manual is available for instructors.

The Biomass Spectrum

A Predator-Prey Theory of Aquatic Production

Author: S. R. Kerr,L. M. Dickie

Publisher: Columbia University Press

ISBN: 9780231507349

Category: Science

Page: 352

View: 4223

Kerr and Dickie propose the development of a new ecological theory, one that can lead to a more effective remedy for the drastic effects of heavy fishing on natural communities of organisms in both marine and freshwater environments. By plotting the densities of the biomass of all organisms in a given community by body-size classes, the authors provide empirical evidence of what they term "the biomass body-size spectrum" in the world's oceans. After examining this evidence, they propose an underlying theory of predator-prey energy transfer: larger species eat smaller species, providing energy exchange across all species within an ecosystem. Providing the first comprehensive synthesis of the energy flow within the biomass spectrum, this book demonstrates not only a new understanding of the self-organizing properties of ecological production systems but also the potential of the biomass spectrum methodology for offering practical remedies when these natural systems are exploited by humans.

Theory Of Difference Equations Numerical Methods And Applications

Author: V. Lakshmikantham,Donato Trigiante

Publisher: CRC Press

ISBN: 0824744241

Category: Mathematics

Page: 320

View: 1963

"Provides a clear and comprehensive overview of the fundamental theories, numerical methods, and iterative processes encountered in difference calculus. Explores classical problems such as orthological polynomials, the Euclidean algorithm, roots of polynomials, and well-conditioning."

Numerical Methods for Structured Matrices and Applications

The Georg Heinig Memorial Volume

Author: Dario Andrea Bini,Volker Mehrmann,Vadim Olshevsky,Eugene Tyrtsyhnikov,Marc van Barel

Publisher: Springer Science & Business Media

ISBN: 9783764389963

Category: Mathematics

Page: 439

View: 2331

This cross-disciplinary volume brings together theoretical mathematicians, engineers and numerical analysts and publishes surveys and research articles related to topics such as fast algorithms, in which the late Georg Heinig made outstanding achievements.