Spectral Methods

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Publisher : Springer Science & Business Media
ISBN 13 : 3540710418
Total Pages : 481 pages
Book Rating : 4.5/5 (47 download)

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Book Synopsis Spectral Methods by : Jie Shen

Download or read book Spectral Methods written by Jie Shen and published by Springer Science & Business Media. This book was released on 2011-08-25 with total page 481 pages. Available in PDF, EPUB and Kindle. Book excerpt: Along with finite differences and finite elements, spectral methods are one of the three main methodologies for solving partial differential equations on computers. This book provides a detailed presentation of basic spectral algorithms, as well as a systematical presentation of basic convergence theory and error analysis for spectral methods. Readers of this book will be exposed to a unified framework for designing and analyzing spectral algorithms for a variety of problems, including in particular high-order differential equations and problems in unbounded domains. The book contains a large number of figures which are designed to illustrate various concepts stressed in the book. A set of basic matlab codes has been made available online to help the readers to develop their own spectral codes for their specific applications.

Spectral Methods

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Publisher : Springer Science & Business Media
ISBN 13 : 3540307265
Total Pages : 585 pages
Book Rating : 4.5/5 (43 download)

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Book Synopsis Spectral Methods by : Claudio Canuto

Download or read book Spectral Methods written by Claudio Canuto and published by Springer Science & Business Media. This book was released on 2007-09-23 with total page 585 pages. Available in PDF, EPUB and Kindle. Book excerpt: Since the publication of "Spectral Methods in Fluid Dynamics" 1988, spectral methods have become firmly established as a mainstream tool for scientific and engineering computation. The authors of that book have incorporated into this new edition the many improvements in the algorithms and the theory of spectral methods that have been made since then. This latest book retains the tight integration between the theoretical and practical aspects of spectral methods, and the chapters are enhanced with material on the Galerkin with numerical integration version of spectral methods. The discussion of direct and iterative solution methods is also greatly expanded.

Spectral Methods in Fluid Dynamics

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Publisher : Springer Science & Business Media
ISBN 13 : 3642841082
Total Pages : 582 pages
Book Rating : 4.6/5 (428 download)

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Book Synopsis Spectral Methods in Fluid Dynamics by : Claudio Canuto

Download or read book Spectral Methods in Fluid Dynamics written by Claudio Canuto and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 582 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is a book about spectral methods for partial differential equations: when to use them, how to implement them, and what can be learned from their of spectral methods has evolved rigorous theory. The computational side vigorously since the early 1970s, especially in computationally intensive of the more spectacular applications are applications in fluid dynamics. Some of the power of these discussed here, first in general terms as examples of the methods have been methods and later in great detail after the specifics covered. This book pays special attention to those algorithmic details which are essential to successful implementation of spectral methods. The focus is on algorithms for fluid dynamical problems in transition, turbulence, and aero dynamics. This book does not address specific applications in meteorology, partly because of the lack of experience of the authors in this field and partly because of the coverage provided by Haltiner and Williams (1980). The success of spectral methods in practical computations has led to an increasing interest in their theoretical aspects, especially since the mid-1970s. Although the theory does not yet cover the complete spectrum of applications, the analytical techniques which have been developed in recent years have facilitated the examination of an increasing number of problems of practical interest. In this book we present a unified theory of the mathematical analysis of spectral methods and apply it to many of the algorithms in current use.

Spectral Methods in Chemistry and Physics

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Publisher : Springer
ISBN 13 : 9401794545
Total Pages : 431 pages
Book Rating : 4.4/5 (17 download)

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Book Synopsis Spectral Methods in Chemistry and Physics by : Bernard Shizgal

Download or read book Spectral Methods in Chemistry and Physics written by Bernard Shizgal and published by Springer. This book was released on 2015-01-07 with total page 431 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is a pedagogical presentation of the application of spectral and pseudospectral methods to kinetic theory and quantum mechanics. There are additional applications to astrophysics, engineering, biology and many other fields. The main objective of this book is to provide the basic concepts to enable the use of spectral and pseudospectral methods to solve problems in diverse fields of interest and to a wide audience. While spectral methods are generally based on Fourier Series or Chebychev polynomials, non-classical polynomials and associated quadratures are used for many of the applications presented in the book. Fourier series methods are summarized with a discussion of the resolution of the Gibbs phenomenon. Classical and non-classical quadratures are used for the evaluation of integrals in reaction dynamics including nuclear fusion, radial integrals in density functional theory, in elastic scattering theory and other applications. The subject matter includes the calculation of transport coefficients in gases and other gas dynamical problems based on spectral and pseudospectral solutions of the Boltzmann equation. Radiative transfer in astrophysics and atmospheric science, and applications to space physics are discussed. The relaxation of initial non-equilibrium distributions to equilibrium for several different systems is studied with the Boltzmann and Fokker-Planck equations. The eigenvalue spectra of the linear operators in the Boltzmann, Fokker-Planck and Schrödinger equations are studied with spectral and pseudospectral methods based on non-classical orthogonal polynomials. The numerical methods referred to as the Discrete Ordinate Method, Differential Quadrature, the Quadrature Discretization Method, the Discrete Variable Representation, the Lagrange Mesh Method, and others are discussed and compared. MATLAB codes are provided for most of the numerical results reported in the book - see Link under 'Additional Information' on the the right-hand column.

Spectral Methods in Surface Superconductivity

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Publisher : Springer Science & Business Media
ISBN 13 : 0817647961
Total Pages : 333 pages
Book Rating : 4.8/5 (176 download)

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Book Synopsis Spectral Methods in Surface Superconductivity by : Søren Fournais

Download or read book Spectral Methods in Surface Superconductivity written by Søren Fournais and published by Springer Science & Business Media. This book was released on 2010-06-15 with total page 333 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book examines in detail the nonlinear Ginzburg–Landau functional, the model most commonly used in the study of superconductivity. Specifically covered are cases in the presence of a strong magnetic field and with a sufficiently large Ginzburg–Landau parameter kappa. Spectral Methods in Surface Superconductivity is intended for students and researchers with a graduate-level understanding of functional analysis, spectral theory, and the analysis of partial differential equations. The book also includes an overview of all nonstandard material as well as important semi-classical techniques in spectral theory that are involved in the nonlinear study of superconductivity.

Implementing Spectral Methods for Partial Differential Equations

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Publisher : Springer Science & Business Media
ISBN 13 : 9048122619
Total Pages : 397 pages
Book Rating : 4.0/5 (481 download)

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Book Synopsis Implementing Spectral Methods for Partial Differential Equations by : David A. Kopriva

Download or read book Implementing Spectral Methods for Partial Differential Equations written by David A. Kopriva and published by Springer Science & Business Media. This book was released on 2009-05-27 with total page 397 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book explains how to solve partial differential equations numerically using single and multidomain spectral methods. It shows how only a few fundamental algorithms form the building blocks of any spectral code, even for problems with complex geometries.

Spectral Analysis of Economic Time Series. (PSME-1)

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Publisher : Princeton University Press
ISBN 13 : 1400875528
Total Pages : 318 pages
Book Rating : 4.4/5 (8 download)

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Book Synopsis Spectral Analysis of Economic Time Series. (PSME-1) by : Clive William John Granger

Download or read book Spectral Analysis of Economic Time Series. (PSME-1) written by Clive William John Granger and published by Princeton University Press. This book was released on 2015-12-08 with total page 318 pages. Available in PDF, EPUB and Kindle. Book excerpt: The important data of economics are in the form of time series; therefore, the statistical methods used will have to be those designed for time series data. New methods for analyzing series containing no trends have been developed by communication engineering, and much recent research has been devoted to adapting and extending these methods so that they will be suitable for use with economic series. This book presents the important results of this research and further advances the application of the recently developed Theory of Spectra to economics. In particular, Professor Hatanaka demonstrates the new technique in treating two problems-business cycle indicators, and the acceleration principle existing in department store data. Originally published in 1964. The Princeton Legacy Library uses the latest print-on-demand technology to again make available previously out-of-print books from the distinguished backlist of Princeton University Press. These editions preserve the original texts of these important books while presenting them in durable paperback and hardcover editions. The goal of the Princeton Legacy Library is to vastly increase access to the rich scholarly heritage found in the thousands of books published by Princeton University Press since its founding in 1905.

Mathematics and the Aesthetic

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Publisher : Springer Science & Business Media
ISBN 13 : 0387381457
Total Pages : 299 pages
Book Rating : 4.3/5 (873 download)

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Book Synopsis Mathematics and the Aesthetic by : Nathalie Sinclair

Download or read book Mathematics and the Aesthetic written by Nathalie Sinclair and published by Springer Science & Business Media. This book was released on 2007-12-28 with total page 299 pages. Available in PDF, EPUB and Kindle. Book excerpt: This collection of essays explores the ancient affinity between the mathematical and the aesthetic, focusing on fundamental connections between these two modes of reasoning and communicating. From historical, philosophical and psychological perspectives, with particular attention to certain mathematical areas such as geometry and analysis, the authors examine ways in which the aesthetic is ever-present in mathematical thinking and contributes to the growth and value of mathematical knowledge.

Spectral Methods for Uncertainty Quantification

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Publisher : Springer Science & Business Media
ISBN 13 : 9048135206
Total Pages : 542 pages
Book Rating : 4.0/5 (481 download)

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Book Synopsis Spectral Methods for Uncertainty Quantification by : Olivier Le Maitre

Download or read book Spectral Methods for Uncertainty Quantification written by Olivier Le Maitre and published by Springer Science & Business Media. This book was released on 2010-03-11 with total page 542 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book deals with the application of spectral methods to problems of uncertainty propagation and quanti?cation in model-based computations. It speci?cally focuses on computational and algorithmic features of these methods which are most useful in dealing with models based on partial differential equations, with special att- tion to models arising in simulations of ?uid ?ows. Implementations are illustrated through applications to elementary problems, as well as more elaborate examples selected from the authors’ interests in incompressible vortex-dominated ?ows and compressible ?ows at low Mach numbers. Spectral stochastic methods are probabilistic in nature, and are consequently rooted in the rich mathematical foundation associated with probability and measure spaces. Despite the authors’ fascination with this foundation, the discussion only - ludes to those theoretical aspects needed to set the stage for subsequent applications. The book is authored by practitioners, and is primarily intended for researchers or graduate students in computational mathematics, physics, or ?uid dynamics. The book assumes familiarity with elementary methods for the numerical solution of time-dependent, partial differential equations; prior experience with spectral me- ods is naturally helpful though not essential. Full appreciation of elaborate examples in computational ?uid dynamics (CFD) would require familiarity with key, and in some cases delicate, features of the associated numerical methods. Besides these shortcomings, our aim is to treat algorithmic and computational aspects of spectral stochastic methods with details suf?cient to address and reconstruct all but those highly elaborate examples.

Spectral Methods for Incompressible Viscous Flow

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Publisher : Springer Science & Business Media
ISBN 13 : 1475765576
Total Pages : 438 pages
Book Rating : 4.4/5 (757 download)

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Book Synopsis Spectral Methods for Incompressible Viscous Flow by : Roger Peyret

Download or read book Spectral Methods for Incompressible Viscous Flow written by Roger Peyret and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 438 pages. Available in PDF, EPUB and Kindle. Book excerpt: This well-written book explains the theory of spectral methods and their application to the computation of viscous incompressible fluid flow, in clear and elementary terms. With many examples throughout, the work will be useful to those teaching at the graduate level, as well as to researchers working in the area.

Spectral Methods in Quantum Field Theory

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Publisher : Springer Science & Business Media
ISBN 13 : 3642001386
Total Pages : 187 pages
Book Rating : 4.6/5 (42 download)

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Book Synopsis Spectral Methods in Quantum Field Theory by : Noah Graham

Download or read book Spectral Methods in Quantum Field Theory written by Noah Graham and published by Springer Science & Business Media. This book was released on 2009-05-08 with total page 187 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this monograph we apply scattering theory methods to calculations in quantum ?eld theory, with a particular focus on properties of the quantum vacuum. These methods will provide e?cient and reliable solutions to a - riety of problems in quantum ?eld theory. Our approach will also elucidate in a concrete context many of the subtleties of quantum ?eld theory, such as divergences, regularization, and renormalization, by connecting them to more familiar results in quantum mechanics. We will use tools of scattering theory to characterize the spectrum of energyeigenstatesinapotentialbackground,hencethetermspectralmethods. This mode spectrum comprises both discrete bound states and a continuum of scattering states. We develop a powerful formalism that parameterizes the e?ects of the continuum by the density of states, which we compute from scattering data. Summing the zero-point energies of these modes gives the energy of the quantum vacuum, which is one of the central quantities we study.Althoughthemostcommonlystudiedbackgroundpotentialsarisefrom static soliton solutions to the classical equations of motion, these methods are not limited to such cases.

Chebyshev and Fourier Spectral Methods

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Publisher : Courier Corporation
ISBN 13 : 0486411834
Total Pages : 690 pages
Book Rating : 4.4/5 (864 download)

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Book Synopsis Chebyshev and Fourier Spectral Methods by : John P. Boyd

Download or read book Chebyshev and Fourier Spectral Methods written by John P. Boyd and published by Courier Corporation. This book was released on 2001-12-03 with total page 690 pages. Available in PDF, EPUB and Kindle. Book excerpt: Completely revised text focuses on use of spectral methods to solve boundary value, eigenvalue, and time-dependent problems, but also covers Hermite, Laguerre, rational Chebyshev, sinc, and spherical harmonic functions, as well as cardinal functions, linear eigenvalue problems, matrix-solving methods, coordinate transformations, methods for unbounded intervals, spherical and cylindrical geometry, and much more. 7 Appendices. Glossary. Bibliography. Index. Over 160 text figures.

Spectral Theory of Value and Actual Economies

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Publisher : Springer Nature
ISBN 13 : 981336260X
Total Pages : 512 pages
Book Rating : 4.8/5 (133 download)

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Book Synopsis Spectral Theory of Value and Actual Economies by : Theodore Mariolis

Download or read book Spectral Theory of Value and Actual Economies written by Theodore Mariolis and published by Springer Nature. This book was released on 2021-05-29 with total page 512 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book develops a unified treatment of the income distribution–capital–value problems with respect to actual economies, and then gradually turns to the issues of effective demand and capitalist accumulation fluctuations from both political economy and economic policy perspectives. That treatment, on the one hand, places produced means of production, positive profits, and capital accumulation at the centre of the analysis and, on the other hand, is analytically based on the modern control theory. Hence, the authors’ investigation is concerned with input–output representations of actual single and joint production, heterogeneous labour, and open economies; zeroes in on the characteristic value distributions of the system matrices; and, finally, derives meaningful theoretical results consistent with the empirical evidence, and vice versa. The main topics addressed are the uncontrollable/unobservable aspects of the real-world economies, the powerful low-order spectral approximations and reconstructions of the inter-industry structure of production–value–distributive variables relationships, the critical-constructive appraisal of both “mainstream” and “radical” theories of value, the matrix demand multipliers and demand-switching policies in heterogeneous capital worlds, and the circular inter-actions amongst income distribution, effective demand, accumulation, and technical conditions of production. Written on the occasion of the 60th anniversary of the publication of both Piero Sraffa’s Production of Commodities by Means of Commodities and Rudolf E. Kalman’s paper “On the general theory of control systems”, this book provides a consistent and comprehensive framework for theoretical, empirical, and economic policy research.

Analysis of Economic Time Series

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Publisher : Academic Press
ISBN 13 : 1483218880
Total Pages : 495 pages
Book Rating : 4.4/5 (832 download)

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Book Synopsis Analysis of Economic Time Series by : Marc Nerlove

Download or read book Analysis of Economic Time Series written by Marc Nerlove and published by Academic Press. This book was released on 2014-05-10 with total page 495 pages. Available in PDF, EPUB and Kindle. Book excerpt: Analysis of Economic Time Series: A Synthesis integrates several topics in economic time-series analysis, including the formulation and estimation of distributed-lag models of dynamic economic behavior; the application of spectral analysis in the study of the behavior of economic time series; and unobserved-components models for economic time series and the closely related problem of seasonal adjustment. Comprised of 14 chapters, this volume begins with a historical background on the use of unobserved components in the analysis of economic time series, followed by an Introduction to the theory of stationary time series. Subsequent chapters focus on the spectral representation and its estimation; formulation of distributed-lag models; elements of the theory of prediction and extraction; and formulation of unobserved-components models and canonical forms. Seasonal adjustment techniques and multivariate mixed moving-average autoregressive time-series models are also considered. Finally, a time-series model of the U.S. cattle industry is presented. This monograph will be of value to mathematicians, economists, and those interested in economic theory, econometrics, and mathematical economics.

Wavelet Applications in Economics and Finance

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Publisher : Springer
ISBN 13 : 3319070614
Total Pages : 271 pages
Book Rating : 4.3/5 (19 download)

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Book Synopsis Wavelet Applications in Economics and Finance by : Marco Gallegati

Download or read book Wavelet Applications in Economics and Finance written by Marco Gallegati and published by Springer. This book was released on 2014-08-04 with total page 271 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book deals with the application of wavelet and spectral methods for the analysis of nonlinear and dynamic processes in economics and finance. It reflects some of the latest developments in the area of wavelet methods applied to economics and finance. The topics include business cycle analysis, asset prices, financial econometrics, and forecasting. An introductory paper by James Ramsey, providing a personal retrospective of a decade's research on wavelet analysis, offers an excellent overview over the field.

Spectral Finite Element Method

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Publisher : Springer Science & Business Media
ISBN 13 : 1846283566
Total Pages : 449 pages
Book Rating : 4.8/5 (462 download)

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Book Synopsis Spectral Finite Element Method by : Srinivasan Gopalakrishnan

Download or read book Spectral Finite Element Method written by Srinivasan Gopalakrishnan and published by Springer Science & Business Media. This book was released on 2007-12-05 with total page 449 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is the first to apply the Spectral Finite Element Method (SFEM) to inhomogeneous and anisotropic structures in a unified and systematic manner. Readers will gain understanding of how to formulate Spectral Finite Element; learn about wave behaviour in inhomogeneous and anisotropic media; and, be able to design some diagnostic tools for monitoring the health of a structure. Tables, figures and graphs support the theory and case studies are included.

The Spectral Analysis of Time Series

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Publisher : Academic Press
ISBN 13 : 1483218546
Total Pages : 383 pages
Book Rating : 4.4/5 (832 download)

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Book Synopsis The Spectral Analysis of Time Series by : L. H. Koopmans

Download or read book The Spectral Analysis of Time Series written by L. H. Koopmans and published by Academic Press. This book was released on 2014-05-12 with total page 383 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Spectral Analysis of Time Series describes the techniques and theory of the frequency domain analysis of time series. The book discusses the physical processes and the basic features of models of time series. The central feature of all models is the existence of a spectrum by which the time series is decomposed into a linear combination of sines and cosines. The investigator can used Fourier decompositions or other kinds of spectrals in time series analysis. The text explains the Wiener theory of spectral analysis, the spectral representation for weakly stationary stochastic processes, and the real spectral representation. The book also discusses sampling, aliasing, discrete-time models, linear filters that have general properties with applications to continuous-time processes, and the applications of multivariate spectral models. The text describes finite parameter models, the distribution theory of spectral estimates with applications to statistical inference, as well as sampling properties of spectral estimates, experimental design, and spectral computations. The book is intended either as a textbook or for individual reading for one-semester or two-quarter course for students of time series analysis users. It is also suitable for mathematicians or professors of calculus, statistics, and advanced mathematics.