1367 records matched your query       

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001 97A7018A403511EB87AA299C42ECA4DB
003 SILO
005 20201217010015
008 190702t20202020flua     b    001 0 eng d
020    $a 0367345471
020    $a 9780367345471
035    $a (OCoLC)1107337512
040    $a YDX $b eng $e rda $c YDX $d YDXIT $d OCLCF $d SILO
050  4 $a QA374 $b .A85 2020
082 04 $a 515.353 $2 23
100 1  $a Atkinson, Kendall E., $e author.
245 10 $a Spectral methods using multivariate polynomials on the unit ball / $c Kendall Atkinson, David Chien, Olaf Hansen.
264  1 $a Boca Raton, FL : $b CRC Press, Taylor & Francis Group, $c [2020]
300    $a xii, 261 pages ; $c 25 cm.
490 1  $a Monographs and research notes in mathematics
520    $a 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.
500    $a "A Chapman & Hall Book" -- title page.
500    $a 8.4 An existence theorem for the three-dimensional Stefan-Boltzmann problem
545 0  $a Kendall Atkinson is Professor Emeritus at University of Iowa as well as Fellow of the Society for Industrial & Applied Mathematics (SIAM). He received his PhD from University of Wisconsin - Madison and has had Faculty appointments at Indiana University, University of Iowa as well as Visiting appointments at Colorado State University, Australian National University, University of New South Wales, University of Queensland. His research interests include numerical analysis, integral equations, multivariate approximation, spectral methods David Chien, PHD, is Professor in the Department of Mathematics at California State University San Marcos. He has authored journal articles in his areas of research interest, which include the numerical solution of integral equations and boundary integral equation methods. Olaf Hansen is Professor of Mathematics, California State University San Marcos. He received his PhD from Johannes Gutenberg University, Mainz, Germany in 1994 and his research interests include Analysis and Numerical Approximation of Boundary and Initial Value Problems and Integral Equations.
504    $a Includes bibliographical references and index.
505 8  $a 3.4 Mapping in three dimensions4. Galerkin's Method for the Dirichlet and Neumann Problems; 4.1 Implementation; 4.1.1 Numerical example; 4.2 Convergence analysis; 4.2.1 The transformed equation; 4.2.2 General theory; 4.2.3 Treating a nonzero Dirichlet boundary condition; 4.3 The Neumann problem; 4.3.1 Implementation; 4.3.2 Numerical example; 4.4 Convergence analysis for the Neumann problem; 4.5 The Neumann problem with y= 0; 4.5.1 Numerical example; 4.5.2 A fluid flow example; 4.5.3 Convergence analysis; 4.6 Defining surface normals and the Jacobian for a general surface
505 8  $a 2.4 A Clenshaw algorithm2.4.1 Implementation; 2.5 Best approximation; 2.6 Quadrature over the unit disk, unit ball, and unit sphere; 2.6.1 Quadrature over the unit sphere; 2.7 Least squares approximation; 2.8 MATLAB programs and numerical examples; 3. Creating Transformations of Regions; 3.1 Constructions of ; 3.1.1 Harmonic mappings; 3.1.2 Using C-modification functions; 3.2 An integration-based mapping formula; 3.2.1 Constructing ; 3.2.2 The integration-based mapping in three dimensions; 3.3 Iteration methods; 3.3.1 The iteration algorithm; 3.3.2 An energy method
505 0  $a 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  $a 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  $a 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
650  0 $a Differential equations, Partial.
650  0 $a Multivariate analysis.
650  0 $a Polynomials.
650  7 $a Differential equations, Partial. $2 fast $0 (OCoLC)fst00893484
650  7 $a Multivariate analysis. $2 fast $0 (OCoLC)fst01029105
650  7 $a Polynomials. $2 fast $0 (OCoLC)fst01070715
776 08 $i Print version: $a Atkinson, Kendall $t Spectral Methods Using Multivariate Polynomials on the Unit Ball $d Milton : CRC Press LLC,c2019 $z 9780367345471
700 1  $a Chien, David, $e author.
700 1  $a Hansen, Olaf, $e author.
830  0 $a Monographs and research notes in mathematics.
941    $a 1
952    $l OVUX522 $d 20220317013319.0
956    $a http://locator.silo.lib.ia.us/search.cgi?index_0=id&term_0=97A7018A403511EB87AA299C42ECA4DB