rdf-syntax-grammar
mods:
  schema location: http://www.loc.gov/mods/v3 http://www.loc.gov/standards/mods/v3/mods-3-2.xsd
  title info:
    title: Implementing Spectral Methods for Partial Differential Equations
    sub title: Algorithms for Scientists and Engineers
  name:
    name part: Kopriva, David A.
    role:
      role term: creator
    role:
      role term: author.
  name:
    name part: SpringerLink (Online service)
  type of resource: text
  origin info:
    place:
      place term: ne
    date issued: 2009
    issuance: monographic
  language:
    language term: eng
  physical description:
    form: electronic
    form: electronic resource
    reformatting quality: access
    form: remote
    extent: XVIII, 397 p. online resource.
  abstract: This book offers a systematic and self-contained approach to solve partial differential equations numerically using single and multidomain spectral methods. It contains detailed algorithms in pseudocode for the application of spectral approximations to both one and two dimensional PDEs of mathematical physics describing potentials, transport, and wave propagation. David Kopriva, a well-known researcher in the field with extensive practical experience, shows how only a few fundamental algorithms form the building blocks of any spectral code, even for problems with complex geometries. The book addresses computational and applications scientists, as it emphasizes the practical derivation and implementation of spectral methods over abstract mathematics. It is divided into two parts: First comes a primer on spectral approximation and the basic algorithms, including FFT algorithms, Gauss quadrature algorithms, and how to approximate derivatives. The second part shows how to use those algorithms to solve steady and time dependent PDEs in one and two space dimensions. Exercises and questions at the end of each chapter encourage the reader to experiment with the algorithms.
  table of contents: Approximating Functions, Derivatives and Integrals -- Spectral Approximation -- Algorithms for Periodic Functions -- Algorithms for Non-Periodic Functions -- Approximating Solutions of PDEs -- Survey of Spectral Approximations -- Spectral Approximation on the Square -- Transformation Methods from Square to Non-Square Geometries -- Spectral Methods in Non-Square Geometries -- Spectral Element Methods -- Erratum -- Erratum.
  note: by David A. Kopriva.
  subject:
    topic: Mathematics
  subject:
    topic: Numerical analysis
  subject:
    topic: Mathematical analysis
  subject:
    topic: Analysis (Mathematics)
  subject:
    topic: Partial differential equations
  subject:
    topic: Applied mathematics
  subject:
    topic: Engineering mathematics
  subject:
    topic: Physics
  subject:
    topic: Mathematics
  subject:
    topic: Partial Differential Equations
  subject:
    topic: Analysis
  subject:
    topic: Applications of Mathematics
  subject:
    topic: Numerical and Computational Physics
  subject:
    topic: Numeric Computing
  subject:
    topic: Theoretical, Mathematical and Computational Physics
  classification: QA370-380
  classification: 515.353
  related item:
    title info:
      title: Springer eBooks
  related item:
    title info:
      title: Scientific Computation
  identifier: 9789048122615
  identifier: http://dx.doi.org/10.1007/978-90-481-2261-5
  record info:
    record creation date: 100301
    record change date: 20151204185537.0
    record identifier: 978-90-481-2261-5