Spectral Methods in Chemistry and Physics - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Spectral Methods in Chemistry and Physics write by Bernard Shizgal. This book was released on 2015-01-07. Spectral Methods in Chemistry and Physics available in PDF, EPUB and Kindle. 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
Spectral Methods - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Spectral Methods write by Claudio Canuto. This book was released on 2007-09-23. Spectral Methods available in PDF, EPUB and Kindle. 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.
Implementing Spectral Methods for Partial Differential Equations
Implementing Spectral Methods for Partial Differential Equations - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Implementing Spectral Methods for Partial Differential Equations write by David A. Kopriva. This book was released on 2009-07-01. Implementing Spectral Methods for Partial Differential Equations available in PDF, EPUB and Kindle. 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
An Introductory Guide to Computational Methods for the Solution of Physics Problems - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook An Introductory Guide to Computational Methods for the Solution of Physics Problems write by George Rawitscher. This book was released on 2018-10-24. An Introductory Guide to Computational Methods for the Solution of Physics Problems available in PDF, EPUB and Kindle. 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.
Spectral Methods of Chemical Analysis
Spectral Methods of Chemical Analysis - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Spectral Methods of Chemical Analysis write by V. Raj. This book was released on 2011-09. Spectral Methods of Chemical Analysis available in PDF, EPUB and Kindle. This book contains all advanced spectroscopic methods which are very very essential to identification of a chemical compound. This book will be useful to Master degree students of chemistry, food science, biochemistry etc. The content of this book is designed in such a way that it will be well suited to graduates and post graduate courses of all science disciplines. To carryout the analysis and identification of a new compound.
