spectral methods in matlab software environments tools

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Spectral Methods In Matlab

Author : Lloyd N. Trefethen
ISBN : 0898719593
Genre : Differential equations, Partial
File Size : 32. 92 MB
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This is the only book on spectral methods built around MATLAB programs. Along with finite differences and finite elements, spectral methods are one of the three main technologies for solving partial differential equations on computers. Since spectral methods involve significant linear algebra and graphics they are very suitable for the high level programming of MATLAB. This hands-on introduction is built around forty short and powerful MATLAB programs, which the reader can download from the World Wide Web.

Chebyshev And Fourier Spectral Methods

Author : John P. Boyd
ISBN : 9780486141923
Genre : Mathematics
File Size : 58. 57 MB
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Completely revised text applies spectral methods to boundary value, eigenvalue, and time-dependent problems, but also covers cardinal functions, matrix-solving methods, coordinate transformations, much more. Includes 7 appendices and over 160 text figures.

Approximation Theory And Approximation Practice

Author : Lloyd N. Trefethen
ISBN : 161197240X
Genre : Mathematics
File Size : 41. 51 MB
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An original and modern treatment of approximation theory for students in applied mathematics. Includes exercises, illustrations and Matlab code.

Spectra And Pseudospectra

Author : Lloyd Nicholas Trefethen
ISBN : 0691119465
Genre : Mathematics
File Size : 62. 45 MB
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Pure and applied mathematicians, physicists, scientists, and engineers use matrices and operators and their eigenvalues in quantum mechanics, fluid mechanics, structural analysis, acoustics, ecology, numerical analysis, and many other areas. However, in some applications the usual analysis based on eigenvalues fails. For example, eigenvalues are often ineffective for analyzing dynamical systems such as fluid flow, Markov chains, ecological models, and matrix iterations. That's where this book comes in. This is the authoritative work on nonnormal matrices and operators, written by the authorities who made them famous. Each of the sixty sections is written as a self-contained essay. Each document is a lavishly illustrated introductory survey of its topic, complete with beautiful numerical experiments and all the right references. The breadth of included topics and the numerous applications that provide links between fields will make this an essential reference in mathematics and related sciences.

Spectral Methods

Author : Jie Shen
ISBN : 9783540710417
Genre : Mathematics
File Size : 60. 21 MB
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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.

Exercises In Computational Mathematics With Matlab

Author : Tom Lyche
ISBN : 9783662435113
Genre : Mathematics
File Size : 63. 2 MB
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Designed to provide tools for independent study, this book contains student-tested mathematical exercises joined with MATLAB programming exercises. Most chapters open with a review followed by theoretical and programming exercises, with detailed solutions provided for all problems including programs. Many of the MATLAB exercises are presented as Russian dolls: each question improves and completes the previous program and results are provided to validate the intermediate programs. The book offers useful MATLAB commands, advice on tables, vectors, matrices and basic commands for plotting. It contains material on eigenvalues and eigenvectors and important norms of vectors and matrices including perturbation theory; iterative methods for solving nonlinear and linear equations; polynomial and piecewise polynomial interpolation; Bézier curves; approximations of functions and integrals and more. The last two chapters considers ordinary differential equations including two point boundary value problems, and deal with finite difference methods for some partial differential equations. The format is designed to assist students working alone, with concise Review paragraphs, Math Hint footnotes on the mathematical aspects of a problem and MATLAB Hint footnotes with tips on programming.

Kernel Based Approximation Methods Using Matlab

Author : Gregory Fasshauer
ISBN : 9789814630153
Genre : Mathematics
File Size : 44. 96 MB
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In an attempt to introduce application scientists and graduate students to the exciting topic of positive definite kernels and radial basis functions, this book presents modern theoretical results on kernel-based approximation methods and demonstrates their implementation in various settings. The authors explore the historical context of this fascinating topic and explain recent advances as strategies to address long-standing problems. Examples are drawn from fields as diverse as function approximation, spatial statistics, boundary value problems, machine learning, surrogate modeling and finance. Researchers from those and other fields can recreate the results within using the documented MATLAB code, also available through the online library. This combination of a strong theoretical foundation and accessible experimentation empowers readers to use positive definite kernels on their own problems of interest.

Finite Difference Methods For Ordinary And Partial Differential Equations

Author : Randall J. LeVeque
ISBN : 0898717833
Genre : Differential equations
File Size : 87. 27 MB
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This book introduces finite difference methods for both ordinary differential equations (ODEs) and partial differential equations (PDEs) and discusses the similarities and differences between algorithm design and stability analysis for different types of equations. A unified view of stability theory for ODEs and PDEs is presented, and the interplay between ODE and PDE analysis is stressed. The text emphasizes standard classical methods, but several newer approaches also are introduced and are described in the context of simple motivating examples.

Parallel Matlab For Multicore And Multinode Computers

Author : Jeremy Kepner
ISBN : 9780898718126
Genre : MATLAB.
File Size : 59. 25 MB
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Parallel MATLAB for Multicore and Multinode Computers is the first book on parallel MATLAB and the first parallel computing book focused on the design, code, debug, and test techniques required to quickly produce well-performing parallel programs. MATLAB is currently the dominant language of technical computing with one million users worldwide, many of whom can benefit from the increased power offered by inexpensive multicore and multinode parallel computers. MATLAB is an ideal environment for learning about parallel computing, allowing the user to focus on parallel algorithms instead of the details of implementation. This book covers more parallel algorithms and parallel programming models than any other parallel programming book due to the succinctness of MATLAB and presents a "hands-on" approach with numerous example programs. Wherever possible, the examples are drawn from widely known and well-documented parallel benchmark codes representative of many real applications.

Spectral Numerical Weather Prediction Models

Author : Martin Ehrendorfer
ISBN : 9781611971989
Genre : Mathematics
File Size : 20. 53 MB
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An explanation of the theory behind the spectral method and its application to building numerical weather prediction models.

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