Spectral Methods Using Multivariate Polynomials On The Unit Ball (inbunden)
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Format
Inbunden (Hardback)
Språk
Engelska
Antal sidor
262
Utgivningsdatum
2019-11-08
Förlag
CRC Press
Illustratör/Fotograf
black and white 10 Tables 103 Line drawings black and white
Illustrationer
103 Line drawings, black and white; 10 Tables, black and white
Antal komponenter
1
ISBN
9780367345471
Spectral Methods Using Multivariate Polynomials On The Unit Ball (inbunden)

Spectral Methods Using Multivariate Polynomials On The Unit Ball

Inbunden Engelska, 2019-11-08
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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.
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Övrig information

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.

Innehållsförteckning

Chapter 1: Introduction Chapter 2: Multivariate Polynomials Chapter 3: Creating Transformations of Regions Chapter 4: Galerkin's method for the Dirichlet and Neumann Problems Chapter 5: Eigenvalue Problems Chapter 6: Parabolic problems Chapter 7: Nonlinear Equations Chapter 8: Nonlinear Neumann Boundary Value Problem Chapter 9: The biharmonic equation Chapter 10: Integral Equations