Spectral Methods Using Multivariate Polynomials on the Unit Ball (Record no. 89981)

MARC details
000 -LEADER
fixed length control field 04938cam a2200637Mu 4500
001 - CONTROL NUMBER
control field 9780429344374
003 - CONTROL NUMBER IDENTIFIER
control field FlBoTFG
005 - DATE AND TIME OF LATEST TRANSACTION
control field 20260210180736.0
006 - FIXED-LENGTH DATA ELEMENTS--ADDITIONAL MATERIAL CHARACTERISTICS--GENERAL INFORMATION
fixed length control field m d
007 - PHYSICAL DESCRIPTION FIXED FIELD--GENERAL INFORMATION
fixed length control field cr cnu---unuuu
008 - FIXED-LENGTH DATA ELEMENTS--GENERAL INFORMATION
fixed length control field 191130s2019 xx o 000 0 eng d
040 ## - CATALOGING SOURCE
Original cataloging agency OCoLC-P
Language of cataloging eng
Transcribing agency OCoLC-P
020 ## - INTERNATIONAL STANDARD BOOK NUMBER
International Standard Book Number 9781000725865
020 ## - INTERNATIONAL STANDARD BOOK NUMBER
International Standard Book Number 1000725863
020 ## - INTERNATIONAL STANDARD BOOK NUMBER
International Standard Book Number 9781000725988
Qualifying information (ePub ebook)
020 ## - INTERNATIONAL STANDARD BOOK NUMBER
International Standard Book Number 1000725987
020 ## - INTERNATIONAL STANDARD BOOK NUMBER
International Standard Book Number 9781000725926
Qualifying information (Mobipocket ebook)
020 ## - INTERNATIONAL STANDARD BOOK NUMBER
International Standard Book Number 1000725928
020 ## - INTERNATIONAL STANDARD BOOK NUMBER
International Standard Book Number 9780429344374
Qualifying information (ebook)
020 ## - INTERNATIONAL STANDARD BOOK NUMBER
International Standard Book Number 0429344376
020 ## - INTERNATIONAL STANDARD BOOK NUMBER
Cancelled/invalid ISBN 0367345471
020 ## - INTERNATIONAL STANDARD BOOK NUMBER
Cancelled/invalid ISBN 9780367345471
024 7# - OTHER STANDARD IDENTIFIER
Standard number or code 10.1201/9780429344374
Source of number or code doi
035 ## - SYSTEM CONTROL NUMBER
System control number (OCoLC)1129224261
Canceled/invalid control number (OCoLC)1129166315
035 ## - SYSTEM CONTROL NUMBER
System control number (OCoLC-P)1129224261
050 #4 - LIBRARY OF CONGRESS CALL NUMBER
Classification number QA374
072 #7 - SUBJECT CATEGORY CODE
Subject category code MAT
Subject category code subdivision 029020
Source bisacsh
072 #7 - SUBJECT CATEGORY CODE
Subject category code MAT
Subject category code subdivision 041000
Source bisacsh
072 #7 - SUBJECT CATEGORY CODE
Subject category code MAT
Subject category code subdivision 007020
Source bisacsh
072 #7 - SUBJECT CATEGORY CODE
Subject category code PBKS
Source bicssc
082 04 - DEWEY DECIMAL CLASSIFICATION NUMBER
Classification number 515.353
Edition number 23
100 1# - MAIN ENTRY--PERSONAL NAME
Personal name Atkinson, Kendall E.
245 10 - TITLE STATEMENT
Title Spectral Methods Using Multivariate Polynomials on the Unit Ball
Medium [electronic resource].
260 ## - PUBLICATION, DISTRIBUTION, ETC. (IMPRINT)
Place of publication, distribution, etc Milton :
Name of publisher, distributor, etc CRC Press LLC,
Date of publication, distribution, etc 2019.
300 ## - PHYSICAL DESCRIPTION
Extent 1 online resource (275 p.).
336 ## -
-- text
-- rdacontent
336 ## -
-- still image
-- rdacontent
337 ## -
-- computer
-- rdamedia
338 ## -
-- online resource
-- rdacarrier
490 1# - SERIES STATEMENT
Series statement Chapman and Hall/CRC Monographs and Research Notes in Mathematics Ser.
500 ## - GENERAL NOTE
General note Description based upon print version of record.
505 0# - FORMATTED CONTENTS NOTE
Formatted contents note Cover; Half Title; Series Page; Title Page; Copyright Page; Dedication; Contents; Preface; 1. Introduction; 1.1 An illustrative example; 1.2 Transformation of the problem; 1.3 Function spaces; 1.4 Variational reformulation; 1.5 A spectral method; 1.6 A numerical example; 1.7 Exterior problems; 1.7.1 Exterior problems in R3; 2. Multivariate Polynomials; 2.1 Multivariate polynomials; 2.2 Triple recursion relation; 2.3 Rapid evaluation of orthonormal polynomials; 2.3.1 Evaluating derivatives for the planar case; 2.3.2 Evaluating derivatives for the three-dimensional case
505 8# - FORMATTED CONTENTS NOTE
Formatted contents note 5. Eigenvalue Problems5.1 Numerical solution -- Dirichlet problem; 5.2 Numerical examples -- Dirichlet problem; 5.3 Convergence analysis -- Dirichlet problem; 5.4 Numerical solution -- Neumann problem; 5.4.1 Numerical examples -- Neumann problem; 6. Parabolic Problems; 6.1 Reformulation and numerical approximation; 6.1.1 Implementation; 6.2 Numerical examples; 6.2.1 An example in three dimensions; 6.3 Convergence analysis; 6.3.1 Further comments; 7. Nonlinear Equations; 7.1 A spectral method for the nonlinear Dirichlet problem; 7.2 Numerical examples; 7.2.1 A three-dimensional example
505 8# - FORMATTED CONTENTS NOTE
Formatted contents note 7.3 Convergence analysis7.3.1 A nonhomogeneous boundary condition; 7.4 Neumann boundary value problem; 7.4.1 Implementation; 7.4.2 Numerical example; 7.4.3 Handling a nonzero Neumann condition; 8. Nonlinear Neumann Boundary Value Problems; 8.1 The numerical method; 8.1.1 Solving the nonlinear system; 8.2 Numerical examples; 8.2.1 Another planar example; 8.2.2 Two three-dimensional examples; 8.3 Error analysis; 8.3.1 The linear Neumann problem; 8.3.2 The nonlinear Neumann problem; 8.3.3 The error over; 8.3.4 A nonhomogeneous boundary value problem
500 ## - GENERAL NOTE
General note 8.4 An existence theorem for the three-dimensional Stefan-Boltzmann problem
520 ## - SUMMARY, ETC.
Summary, etc Spectral Methods Using Multivariate Polynomials on the Unit Ball is a research level text on a numerical method for the solution of partial differential equations. The authors introduce, illustrate with examples, and analyze 'spectral methods' that are based on multivariate polynomial approximations. The method presented is an alternative to finite element and difference methods for regions that are diffeomorphic to the unit disk, in two dimensions, and the unit ball, in three dimensions. The speed of convergence of spectral methods is usually much higher than that of finite element or finite difference methods. Features Introduces the use of multivariate polynomials for the construction and analysis of spectral methods for linear and nonlinear boundary value problems Suitable for researchers and students in numerical analysis of PDEs, along with anyone interested in applying this method to a particular physical problem One of the few texts to address this area using multivariate orthogonal polynomials, rather than tensor products of univariate polynomials.
588 ## -
-- OCLC-licensed vendor bibliographic record.
650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM
Topical term or geographic name as entry element Differential equations, Partial.
650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM
Topical term or geographic name as entry element Multivariate analysis.
650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM
Topical term or geographic name as entry element Polynomials.
650 #7 - SUBJECT ADDED ENTRY--TOPICAL TERM
Topical term or geographic name as entry element MATHEMATICS / Probability & Statistics / Multivariate Analysis
Source of heading or term bisacsh
700 1# - ADDED ENTRY--PERSONAL NAME
Personal name Chien, David.
700 1# - ADDED ENTRY--PERSONAL NAME
Personal name Hansen, Olaf.
856 40 - ELECTRONIC LOCATION AND ACCESS
Materials specified Taylor & Francis
Uniform Resource Identifier <a href="https://www.taylorfrancis.com/books/9780429344374">https://www.taylorfrancis.com/books/9780429344374</a>
856 42 - ELECTRONIC LOCATION AND ACCESS
Materials specified OCLC metadata license agreement
Uniform Resource Identifier <a href="http://www.oclc.org/content/dam/oclc/forms/terms/vbrl-201703.pdf">http://www.oclc.org/content/dam/oclc/forms/terms/vbrl-201703.pdf</a>

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