Numerical Methods that Work

Author: Forman S. Acton

Publisher: MAA

ISBN: 9780883854501

Category: Mathematics

Page: 549

View: 5654

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

Numerical Methods in Fluid Mechanics

Author: Alain Vincent

Publisher: American Mathematical Soc.

ISBN: 9780821808139

Category: Science

Page: 199

View: 2543

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 of Exploration Seismology

With Algorithms in MATLAB®

Author: Gary F. Margrave,Michael P. Lamoureux

Publisher: Cambridge University Press

ISBN: 1107170141

Category: Business & Economics

Page: 472

View: 7687

Technical guide to the theory and practice of seismic data processing with MATLAB algorithms for advanced students, researchers and professionals.

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: 1915

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.

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: 1301

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.

Applied Numerical Methods Using MATLAB

Author: Won Y. Yang,Wenwu Cao,Tae-Sang Chung,John Morris

Publisher: John Wiley & Sons

ISBN: 0471705187

Category: Mathematics

Page: 400

View: 9952

In recent years, with the introduction of new media products, therehas been a shift in the use of programming languages from FORTRANor C to MATLAB for implementing numerical methods. This book makesuse of the powerful MATLAB software to avoid complex derivations,and to teach the fundamental concepts using the software to solvepractical problems. Over the years, many textbooks have beenwritten on the subject of numerical methods. Based on their courseexperience, the authors use a more practical approach and linkevery method to real engineering and/or science problems. The mainbenefit is that engineers don't have to know the mathematicaltheory in order to apply the numerical methods for solving theirreal-life problems. An Instructor's Manual presenting detailed solutions to all theproblems in the book is available online.

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: 9264

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.

Recent Advances in Numerical Methods and Applications II

Author: Oleg P Iliev,Mikhail S Kaschiev,Svetozar D Margenov,Blagovest H Sendov,Panayot S Vassilevski

Publisher: World Scientific

ISBN: 9814531855


Page: 924

View: 3607

This volume contains the proceedings of the 4th International Conference on Numerical Methods and Applications. The major topics covered include: general finite difference, finite volume, finite element and boundary element methods, general numerical linear algebra and parallel computations, numerical methods for nonlinear problems and multiscale methods, multigrid and domain decomposition methods, CFD computations, mathematical modeling in structural mechanics, and environmental and engineering applications. The volume reflects the current research trends in the specified areas of numerical methods and their applications. Contents: Computational Issues in Large Scale Eigenvalue ProblemsCombustion Modeling in Industrial FurnacesMonte Carlo MethodsMultilevel Methods for Incompressible Viscous FlowsApproximation of Nonlinear and Functional PDEsSolving Linear Systems with Error ControlRegular Numerical Methods for Inverse and Ill-Posed ProblemsMultifield ProblemsParallel and Distributed Numerical Computing with ApplicationsParameter-Robust Numerical Methods for Singularly Perturbed and Convection-Dominated ProblemsFinite Difference MethodsFinite Element MethodsFinite Volume MethodsBoundary Element MethodsNumerical Linear AlgebraNumerical Methods for Nonlinear ProblemsNumerical Methods for Multiscale ProblemsMultigrid and Domain DecompositionComputational Fluid DynamicsMathematical Modelling in Structural MechanicsEnvironmental ModellingEngineering Applications Readership: Researchers in applied mathematics and computational physics. Keywords:Numerical Methods and Applications;General Finite Difference;General Numerical Linear Algebra;Parallel Computations;Nonlinear Problems and Multiscale Methods

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: 8414

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.

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: 7813

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.

Theory Of Difference Equations Numerical Methods And Applications

Author: V. Lakshmikantham,Donato Trigiante

Publisher: CRC Press

ISBN: 0824744241

Category: Mathematics

Page: 320

View: 4122

"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."

Complex Effects in Large Eddy Simulations

Author: Stavros Kassinos,Carlos Langer,Gianluca Iaccarino,Parviz Moin

Publisher: Springer Science & Business Media

ISBN: 3540342346

Category: Technology & Engineering

Page: 446

View: 5987

The field of Large Eddy Simulations is reaching a level of maturity that brings this approach to the mainstream of engineering computations, while it opens opportunities and challenges. The main objective of this volume is to bring together leading experts in presenting the state-of-the-art and emerging approaches for treating complex effects in LES. A common theme throughout is the role of LES in the context of multiscale modeling and simulation.

Theory of Difference Equations Numerical Methods and Applications by V Lakshmikantham and D Trigiante

Author: Lakshmikantham,D. Trigiante

Publisher: Elsevier

ISBN: 9780080958699

Category: Mathematics

Page: 322

View: 7435

In this book, we study theoretical and practical aspects of computing methods for mathematical modelling of nonlinear systems. A number of computing techniques are considered, such as methods of operator approximation with any given accuracy; operator interpolation techniques including a non-Lagrange interpolation; methods of system representation subject to constraints associated with concepts of causality, memory and stationarity; methods of system representation with an accuracy that is the best within a given class of models; methods of covariance matrix estimation; methods for low-rank matrix approximations; hybrid methods based on a combination of iterative procedures and best operator approximation; and methods for information compression and filtering under condition that a filter model should satisfy restrictions associated with causality and different types of memory. As a result, the book represents a blend of new methods in general computational analysis, and specific, but also generic, techniques for study of systems theory ant its particular branches, such as optimal filtering and information compression. - Best operator approximation, - Non-Lagrange interpolation, - Generic Karhunen-Loeve transform - Generalised low-rank matrix approximation - Optimal data compression - Optimal nonlinear filtering

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: 3086

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.

Thermal Radiation Heat Transfer, Fourth Edition

Author: Robert Siegel

Publisher: CRC Press

ISBN: 9781560328391

Category: Technology & Engineering

Page: 864

View: 2885

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.

Computational Methods in Finance

Author: Ali Hirsa

Publisher: CRC Press

ISBN: 1466576049

Category: Business & Economics

Page: 444

View: 1230

As today’s financial products have become more complex, quantitative analysts, financial engineers, and others in the financial industry now require robust techniques for numerical analysis. Covering advanced quantitative techniques, Computational Methods in Finance explains how to solve complex functional equations through numerical methods. The first part of the book describes pricing methods for numerous derivatives under a variety of models. The book reviews common processes for modeling assets in different markets. It then examines many computational approaches for pricing derivatives. These include transform techniques, such as the fast Fourier transform, the fractional fast Fourier transform, the Fourier-cosine method, and saddlepoint method; the finite difference method for solving PDEs in the diffusion framework and PIDEs in the pure jump framework; and Monte Carlo simulation. The next part focuses on essential steps in real-world derivative pricing. The author discusses how to calibrate model parameters so that model prices are compatible with market prices. He also covers various filtering techniques and their implementations and gives examples of filtering and parameter estimation. Developed from the author’s courses at Columbia University and the Courant Institute of New York University, this self-contained text is designed for graduate students in financial engineering and mathematical finance as well as practitioners in the financial industry. It will help readers accurately price a vast array of derivatives.

Mathematical and Computational Methods for Compressible Flow

Author: Miloslav Feistauer,Jiří Felcman,Ivan Straškraba

Publisher: Oxford University Press on Demand

ISBN: 9780198505884

Category: Mathematics

Page: 535

View: 1909

This book is concerned with mathematical and numerical methods for compressible flow. It aims to provide the reader with a sufficiently detailed and extensive, mathematically precise, but comprehensible guide, through a wide spectrum of mathematical and computational methods used in Computational Fluid Dynamics (CFD) for the numerical simulation of compressible flow. Up-to-date techniques applied in the numerical solution of inviscid as well as viscous compressible flow on unstructured meshes are explained, thus allowing the simulation of complex three-dimensional technically relevant problems. Among some of the methods addressed are finite volume methods using approximate Riemann solvers, finite element techniques, such as the streamline diffusion and the discontinuous Galerkin methods, and combined finite volume - finite element schemes. The book gives a complex insight into the numerics of compressible flow, covering the development of numerical schemes and their theoretical mathematical analysis, their verification on test problems and use in solving practical engineering problems. The book will be helpful to specialists coming into contact with CFD - pure and applied mathematicians, aerodynamists, engineers, physicists and natural scientists. It will also be suitable for advanced undergraduate, graduate and postgraduate students of mathematics and technical sciences.