Spectral Methods In Matlab
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Spectral Methods In Matlab
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Author : Lloyd N. Trefethen
language : en
Publisher: SIAM
Release Date : 2000-07-01
Spectral Methods In Matlab written by Lloyd N. Trefethen and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 2000-07-01 with Mathematics categories.
Mathematics of Computing -- Numerical Analysis.
Spectral Methods
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Author : Claudio Canuto
language : en
Publisher: Springer Science & Business Media
Release Date : 2007-09-23
Spectral Methods written by Claudio Canuto 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 2007-09-23 with Science categories.
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 For Time Dependent Problems
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Author : Jan S. Hesthaven
language : en
Publisher: Cambridge University Press
Release Date : 2007-01-11
Spectral Methods For Time Dependent Problems written by Jan S. Hesthaven and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-01-11 with Mathematics categories.
Spectral methods are well-suited to solve problems modeled by time-dependent partial differential equations: they are fast, efficient and accurate and widely used by mathematicians and practitioners. This class-tested 2007 introduction, the first on the subject, is ideal for graduate courses, or self-study. The authors describe the basic theory of spectral methods, allowing the reader to understand the techniques through numerous examples as well as more rigorous developments. They provide a detailed treatment of methods based on Fourier expansions and orthogonal polynomials (including discussions of stability, boundary conditions, filtering, and the extension from the linear to the nonlinear situation). Computational solution techniques for integration in time are dealt with by Runge-Kutta type methods. Several chapters are devoted to material not previously covered in book form, including stability theory for polynomial methods, techniques for problems with discontinuous solutions, round-off errors and the formulation of spectral methods on general grids. These will be especially helpful for practitioners.
Spectral Methods For Non Standard Eigenvalue Problems
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Author : Călin-Ioan Gheorghiu
language : en
Publisher: Springer Science & Business
Release Date : 2014-04-22
Spectral Methods For Non Standard Eigenvalue Problems written by Călin-Ioan Gheorghiu and has been published by Springer Science & Business this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-04-22 with Mathematics categories.
This book focuses on the constructive and practical aspects of spectral methods. It rigorously examines the most important qualities as well as drawbacks of spectral methods in the context of numerical methods devoted to solve non-standard eigenvalue problems. In addition, the book also considers some nonlinear singularly perturbed boundary value problems along with eigenproblems obtained by their linearization around constant solutions. The book is mathematical, poising problems in their proper function spaces, but its emphasis is on algorithms and practical difficulties. The range of applications is quite large. High order eigenvalue problems are frequently beset with numerical ill conditioning problems. The book describes a wide variety of successful modifications to standard algorithms that greatly mitigate these problems. In addition, the book makes heavy use of the concept of pseudospectrum, which is highly relevant to understanding when disaster is imminent in solving eigenvalue problems. It also envisions two classes of applications, the stability of some elastic structures and the hydrodynamic stability of some parallel shear flows. This book is an ideal reference text for professionals (researchers) in applied mathematics, computational physics and engineering. It will be very useful to numerically sophisticated engineers, physicists and chemists. The book can also be used as a textbook in review courses such as numerical analysis, computational methods in various engineering branches or physics and computational methods in analysis.
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.
Computational Methods In Physics
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Author : Simon Širca
language : en
Publisher: Springer Nature
Release Date : 2025-04-01
Computational Methods In Physics written by Simon Širca and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-04-01 with Science categories.
This textbook provides a compendium of numerical methods to assist physics students and researchers in their daily work. It carefully considers error estimates, stability and convergence issues, the choice of optimal methods, and techniques to increase program execution speeds. The book supplies numerous examples throughout the chapters that are concluded by more comprehensive problems with a strong physics background. Instead of uncritically employing modern black-box tools, the readers are encouraged to develop a more ponderous and skeptical approach. This revised and expanded edition now includes a new chapter on numerical integration and stable differentiation, as well as fresh material on optimal filtering, integration of gravitational many-body problems, computation of Poincaré maps, regularization of orbits, singular Sturm-Liouville problems, techniques for time evolution and spatial treatment of (semi)infinite domains in spectral methods, and phase retrieval. It also brings updated discussions of algebraic problems involving sparse matrices and of high-resolution schemes for partial differential equations.
Chebyshev And Fourier Spectral Methods
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Author : John P. Boyd
language : en
Publisher: Courier Corporation
Release Date : 2001-12-03
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 2001-12-03 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.
An Introduction To Numerical Methods And Analysis
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Author : James F. Epperson
language : en
Publisher: John Wiley & Sons
Release Date : 2021-07-21
An Introduction To Numerical Methods And Analysis written by James F. Epperson 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 2021-07-21 with Mathematics categories.
The new edition of the popular introductory textbook on numerical approximation methods and mathematical analysis, with a unique emphasis on real-world application An Introduction to Numerical Methods and Analysis helps students gain a solid understanding of a wide range of numerical approximation methods for solving problems of mathematical analysis. Designed for entry-level courses on the subject, this popular textbook maximizes teaching flexibility by first covering basic topics before gradually moving to more advanced material in each chapter and section. Throughout the text, students are provided clear and accessible guidance on a wide range of numerical methods and analysis techniques, including root-finding, numerical integration, interpolation, solution of systems of equations, and many others. This fully revised third edition contains new sections on higher-order difference methods, the bisection and inertia method for computing eigenvalues of a symmetric matrix, a completely re-written section on different methods for Poisson equations, and spectral methods for higher-dimensional problems. New problem sets—ranging in difficulty from simple computations to challenging derivations and proofs—are complemented by computer programming exercises, illustrative examples, and sample code. This acclaimed textbook: Explains how to both construct and evaluate approximations for accuracy and performance Covers both elementary concepts and tools and higher-level methods and solutions Features new and updated material reflecting new trends and applications in the field Contains an introduction to key concepts, a calculus review, an updated primer on computer arithmetic, a brief history of scientific computing, a survey of computer languages and software, and a revised literature review Includes an appendix of proofs of selected theorems and a companion website with additional exercises, application models, and supplemental resources An Introduction to Numerical Methods and Analysis, Third Edition is the perfect textbook for upper-level undergraduate students in mathematics, science, and engineering courses, as well as for courses in the social sciences, medicine, and business with numerical methods and analysis components.
Theory And Applications Of Gaussian Quadrature Methods
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Author : Narayan Kovvali
language : en
Publisher: Springer Nature
Release Date : 2022-05-31
Theory And Applications Of Gaussian Quadrature Methods written by Narayan Kovvali and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-05-31 with Technology & Engineering categories.
Gaussian quadrature is a powerful technique for numerical integration that falls under the broad category of spectral methods. The purpose of this work is to provide an introduction to the theory and practice of Gaussian quadrature. We study the approximation theory of trigonometric and orthogonal polynomials and related functions and examine the analytical framework of Gaussian quadrature. We discuss Gaussian quadrature for bandlimited functions, a topic inspired by some recent developments in the analysis of prolate spheroidal wave functions. Algorithms for the computation of the quadrature nodes and weights are described. Several applications of Gaussian quadrature are given, ranging from the evaluation of special functions to pseudospectral methods for solving differential equations. Software realization of select algorithms is provided. Table of Contents: Introduction / Approximating with Polynomials and Related Functions / Gaussian Quadrature / Applications / Links to Mathematical Software
Numerical Methods For Diffusion Phenomena In Building Physics
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Author : Nathan Mendes
language : en
Publisher: PUCPRess
Release Date : 2017-05-19
Numerical Methods For Diffusion Phenomena In Building Physics written by Nathan Mendes and has been published by PUCPRess this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-05-19 with Science categories.
This book intends to stimulate research in simulation of diff usion problems in building physics, by fi rst providing an overview of mathematical models and numerical techniques such as the fi nitediff erence and fi nite-element methods traditionally used in building simulation tools. Then, nonconventional methods such as reduced order models, boundary integral approaches and spectral methods are presented, which might be considered in the next generation of building-energy-simulation tools. The advantage of these methods includes the improvement of the numerical solution of diff usion phenomena, especially in large domains relevant to building energy performance analysis.