| Document Type
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BL
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| Record Number
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1041215
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| Doc. No
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b795585
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| Main Entry
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Fornberg, Bengt.
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| Title & Author
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A practical guide to pseudospectral methods /\ Bengt Fornberg.
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| Publication Statement
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Cambridge ;New York :: Cambridge University Press,, 1996.
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| Series Statement
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Cambridge monographs on applied and computational mathematics ;; 1
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| Page. NO
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x, 231 pages :: illustrations ;; 24 cm.
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| ISBN
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0521495822
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: 9780521495820
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| Bibliographies/Indexes
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Includes bibliographical references (pages 217-228) and index.
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| Contents
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1. Introduction -- 2. Introduction to spectral methods via orthogonal functions -- 3. Introduction to PS methods via finite differences -- 4. Key properties of PS approximations -- 5. PS variations and enhancements -- 6. PS methods in polar and spherical geometries -- 7. Comparisons of computational cost for FD and PS methods -- 8. Applications for spectral methods -- App. A: Jacobi polynomials -- App. B: Tau, Galerkin, and collocation (PS) implementations -- App. C: Codes for algorithm to find FD weights -- App. D: Lebesgue constants -- App. E: Potential function estimate for polynomial interpolation error -- App. F: FFT-based implementation of PS methods -- App. G: Stability domains for some ODE solvers -- App. H: Energy estimates.
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| Abstract
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Partial differential equations arise in almost all areas of science, engineering, modeling, and forecasting. During the last two decades, pseudospectral methods have emerged as successful, and often superior, alternatives to better-known computational procedures - such as finite difference and finite element methods - in several key application areas. These areas include computational fluid dynamics, wave motion, and weather forecasting. This book explains how, when, and why this pseudospectral approach works. In order to make the subject accessible to students as well as to researchers and engineers, the presentation incorporates illustrations, examples, heuristic explanations, and algorithms rather than rigorous theoretical arguments. A key theme of the book is to establish and exploit the close connection that exists between pseudospectral and finite difference methods.
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This approach not only leads to new insights into already established pseudospectral procedures, but also provides many novel and powerful pseudospectral variations. This book will be of interest to graduate students, scientists, and engineers interested in applying pseudospectral methods to real problems.
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| Subject
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Finite differences.
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| Subject
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Spectral theory (Mathematics)
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31.46 functional analysis.
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| Subject
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Differential equations-- Numerical solutions.
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| Subject
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Finite differences.
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| Subject
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Finite differences.
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| Subject
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Spectral theory (Mathematics)
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Spectraaltheorie.
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| Dewey Classification
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515/.7242
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| LC Classification
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QA320.F65 1996
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| NLM classification
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31.46bcl
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