Spectral Methods In Chemistry And Physics

Author : Bernard Shizgal
Publisher : Springer
ISBN 13 : 9401794545
Total Pages : 431 pages
Book Rating : 4.41/5 ( download)

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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.

Author : George Rawitscher
Publisher : Springer
ISBN 13 : 3319427032
Total Pages : 221 pages
Book Rating : 4.34/5 ( download)

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Download or read book An Introductory Guide to Computational Methods for the Solution of Physics Problems written by George Rawitscher and published by Springer. This book was released on 2018-10-24 with total page 221 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Author : David A. Kopriva
Publisher :
ISBN 13 : 9783540927419
Total Pages : 350 pages
Book Rating : 4.17/5 ( download)

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Download or read book Implementing Spectral Methods for Partial Differential Equations written by David A. Kopriva and published by . This book was released on 2009-07-01 with total page 350 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Author : Olivier Le Maitre
Publisher : Springer Science & Business Media
ISBN 13 : 9048135206
Total Pages : 542 pages
Book Rating : 4.02/5 ( download)

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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.

Author : John P. Boyd
Publisher : Courier Corporation
ISBN 13 : 0486141926
Total Pages : 690 pages
Book Rating : 4.23/5 ( download)

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Download or read book Chebyshev and Fourier Spectral Methods written by John P. Boyd and published by Courier Corporation. This book was released on 2013-06-05 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.

Author : Peter Pelikan
Publisher : CRC Press
ISBN 13 : 1000142078
Total Pages : 360 pages
Book Rating : 4.75/5 ( download)

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Download or read book Applications of Numerical Methods in Molecular Spectroscopy written by Peter Pelikan and published by CRC Press. This book was released on 2020-11-25 with total page 360 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Author : John P. Boyd
Publisher : Courier Corporation
ISBN 13 : 0486411834
Total Pages : 690 pages
Book Rating : 4.35/5 ( download)

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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.

Author : Jamal Amani Rad
Publisher : Springer Nature
ISBN 13 : 9811965536
Total Pages : 312 pages
Book Rating : 4.31/5 ( download)

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Download or read book Learning with Fractional Orthogonal Kernel Classifiers in Support Vector Machines written by Jamal Amani Rad and published by Springer Nature. This book was released on 2023-03-18 with total page 312 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book contains select chapters on support vector algorithms from different perspectives, including mathematical background, properties of various kernel functions, and several applications. The main focus of this book is on orthogonal kernel functions, and the properties of the classical kernel functions—Chebyshev, Legendre, Gegenbauer, and Jacobi—are reviewed in some chapters. Moreover, the fractional form of these kernel functions is introduced in the same chapters, and for ease of use for these kernel functions, a tutorial on a Python package named ORSVM is presented. The book also exhibits a variety of applications for support vector algorithms, and in addition to the classification, these algorithms along with the introduced kernel functions are utilized for solving ordinary, partial, integro, and fractional differential equations. On the other hand, nowadays, the real-time and big data applications of support vector algorithms are growing. Consequently, the Compute Unified Device Architecture (CUDA) parallelizing the procedure of support vector algorithms based on orthogonal kernel functions is presented. The book sheds light on how to use support vector algorithms based on orthogonal kernel functions in different situations and gives a significant perspective to all machine learning and scientific machine learning researchers all around the world to utilize fractional orthogonal kernel functions in their pattern recognition or scientific computing problems.

Author :
Publisher :
ISBN 13 :
Total Pages : 806 pages
Book Rating : 4.89/5 ( download)

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Download or read book Energy Research Abstracts written by and published by . This book was released on 1992 with total page 806 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Author : C. Canuto
Publisher :
ISBN 13 :
Total Pages : 592 pages
Book Rating : 4.74/5 ( download)

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Download or read book Spectral Methods in Fluid Dynamics written by C. Canuto and published by . This book was released on 1988 with total page 592 pages. Available in PDF, EPUB and Kindle. Book excerpt: