Spectral Methods In Chemistry And Physics
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Spectral Methods In Chemistry And Physics
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Author : Bernard Shizgal
language : en
Publisher: Springer
Release Date : 2015-01-07
Spectral Methods In Chemistry And Physics written by Bernard Shizgal and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-01-07 with Science categories.
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 For Uncertainty Quantification
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Author : Olivier Le Maitre
language : en
Publisher: Springer Science & Business Media
Release Date : 2010-03-11
Spectral Methods For Uncertainty Quantification written by Olivier Le Maitre and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-03-11 with Science categories.
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.
Implementing Spectral Methods For Partial Differential Equations
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Author : David A. Kopriva
language : en
Publisher:
Release Date : 2009-07-01
Implementing Spectral Methods For Partial Differential Equations written by David A. Kopriva and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-07-01 with Science categories.
This book presents a systematic development of the fundamental algorithms needed to write spectral methods codes to solve basic problems of mathematical physics: Steady potentials, transport, and wave propagation. It shows that only a few fundamental algorithms for interpolation, differentiation and the FFT form the building blocks of any spectral code, even for problems in complex geometries. The algorithms approximate problems in 1D and 2D to show the flexibility of spectral methods, and to make the transition from exploratory to application codes as straightforward as possible. The book serves as a textbook for graduate students and as a starting point for applications scientists.
An Introductory Guide To Computational Methods For The Solution Of Physics Problems
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Author : George Rawitscher
language : en
Publisher: Springer
Release Date : 2018-10-24
An Introductory Guide To Computational Methods For The Solution Of Physics Problems written by George Rawitscher and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-10-24 with Science categories.
This monograph presents fundamental aspects of modern spectral and other computational methods, which are not generally taught in traditional courses. It emphasizes concepts as errors, convergence, stability, order and efficiency applied to the solution of physical problems. The spectral methods consist in expanding the function to be calculated into a set of appropriate basis functions (generally orthogonal polynomials) and the respective expansion coefficients are obtained via collocation equations. The main advantage of these methods is that they simultaneously take into account all available information, rather only the information available at a limited number of mesh points. They require more complicated matrix equations than those obtained in finite difference methods. However, the elegance, speed, and accuracy of the spectral methods more than compensates for any such drawbacks. During the course of the monograph, the authors examine the usually rapid convergence of the spectral expansions and the improved accuracy that results when nonequispaced support points are used, in contrast to the equispaced points used in finite difference methods. In particular, they demonstrate the enhanced accuracy obtained in the solutionof integral equations. The monograph includes an informative introduction to old and new computational methods with numerous practical examples, while at the same time pointing out the errors that each of the available algorithms introduces into the specific solution. It is a valuable resource for undergraduate students as an introduction to the field and for graduate students wishing to compare the available computational methods. In addition, the work develops the criteria required for students to select the most suitable method to solve the particular scientific problem that they are confronting.
Applications Of Numerical Methods In Molecular Spectroscopy
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Author : Peter Pelikan
language : en
Publisher: CRC Press
Release Date : 2020-11-25
Applications Of Numerical Methods In Molecular Spectroscopy written by Peter Pelikan and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-11-25 with Science categories.
Applications of Numerical Methods in Molecular Spectroscopy provides a mathematical background, theoretical perspective, and review of spectral data processing methods. The book discusses methods of complex spectral profile separation into bands, factor analysis methods, methods of quantitative analysis in molecular spectroscopy and reflectance spectroscopy, and new data processing methods. Mathematical methods in special areas of molecular spectroscopy, such as color science, electron spin resonance, and nuclear magnetic resonance spectroscopies are also covered. The book will benefit researchers and postgraduate students in fields of chemistry, physics, and biology.
Nonlinear Methods Of Spectral Analysis
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Author : S. Haykin
language : en
Publisher:
Release Date : 2014-01-15
Nonlinear Methods Of Spectral Analysis written by S. Haykin and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-01-15 with categories.
Mathematical Analysis And Numerical Methods For Science And Technology
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Author : Robert Dautray
language : en
Publisher: Springer Science & Business Media
Release Date : 1999-11-23
Mathematical Analysis And Numerical Methods For Science And Technology written by Robert Dautray and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 1999-11-23 with Mathematics categories.
The advent of high-speed computers has made it possible for the first time to calculate values from models accurately and rapidly. Researchers and engineers thus have a crucial means of using numerical results to modify and adapt arguments and experiments along the way. Every facet of technical and industrial activity has been affected by these developments. The objective of the present work is to compile the mathematical knowledge required by researchers in mechanics, physics, engineering, chemistry and other branches of application of mathematics for the theoretical and numerical resolution of physical models on computers. Since the publication in 1924 of the "Methoden der mathematischen Physik" by Courant and Hilbert, there has been no other comprehensive and up-to-date publication presenting the mathematical tools needed in applications of mathematics in directly implementable form.
Chebyshev And Fourier Spectral Methods
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Author : John P. Boyd
language : en
Publisher: Courier Corporation
Release Date : 2013-06-05
Chebyshev And Fourier Spectral Methods written by John P. Boyd and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-06-05 with Mathematics categories.
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.
Fractional Order Analysis
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Author : Hemen Dutta
language : en
Publisher: John Wiley & Sons
Release Date : 2020-08-06
Fractional Order Analysis written by Hemen Dutta and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-08-06 with Mathematics categories.
A guide to the new research in the field of fractional order analysis Fractional Order Analysis contains the most recent research findings in fractional order analysis and its applications. The authors—noted experts on the topic—offer an examination of the theory, methods, applications, and the modern tools and techniques in the field of fractional order analysis. The information, tools, and applications presented can help develop mathematical methods and models with better accuracy. Comprehensive in scope, the book covers a range of topics including: new fractional operators, fractional derivatives, fractional differential equations, inequalities for different fractional derivatives and fractional integrals, fractional modeling related to transmission of Malaria, and dynamics of Zika virus with various fractional derivatives, and more. Designed to be an accessible text, several useful, relevant and connected topics can be found in one place, which is crucial for an understanding of the research problems of an applied nature. This book: Contains recent development in fractional calculus Offers a balance of theory, methods, and applications Puts the focus on fractional analysis and its interdisciplinary applications, such as fractional models for biological models Helps make research more relevant to real-life applications Written for researchers, professionals and practitioners, Fractional Order Analysis offers a comprehensive resource to fractional analysis and its many applications as well as information on the newest research.
Chemical Analysis
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Author : Francis Rouessac
language : en
Publisher: Wiley
Release Date : 2000-06-21
Chemical Analysis written by Francis Rouessac and has been published by Wiley this book supported file pdf, txt, epub, kindle and other format this book has been release on 2000-06-21 with Science categories.
Chemical Analysis is an essential introduction to a wide range of analytical techniques and instruments. Assuming little in the way of prior knowledge, this text carefully guides the reader through the more widely used and important techniques, whilst avoiding excessive technical detail. Covering both instrumental techniques and the situations in which they are used, the text always strives to maintain a balance between breadth and depth of coverage. Carefully structured, this book clearly differentiates between separation and spectral methods, and includes a section on more specialised techniques. Chemical Analysis * Provides a through introduction to a wide range of the most important and widely used instrumental techniques. * Maintains a careful balance between depth and breadth of coverage. * Includes many examples, problems and their solutions. Chemical Analysis will be invaluable to those studying or using instrumental techniques throughout the sciences, medicine and engineering.