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: Mathematical aspects of numerical solution of hyperbolic systems
  title info:
    title: MATHnetBASE
  name:
    name part: Kulikovskiĭ, A. G. (Andreĭ Gennadievich)
    role:
      role term: creator
    role:
      role term: eauthor.
  name:
    name part: Pogorelov, N. V. (Nikolai V.)
    role:
      role term: author.
  name:
    name part: Semenov, A. Yu. (Andrei Yurievich)
    name part: 1955-
    role:
      role term: author.
  name:
    name part: Taylor & Francis
  name:
    name part: Taylor and Francis
  type of resource: text
  genre: bibliography
  genre: Electronic books.
  origin info:
    place:
      place term: flu
    date issued: 2000
    edition: First edition.
    issuance: monographic
  language:
    language term: eng
  physical description:
    form: remote
    extent: 1 online resource (560 pages) : 1 illustrations.
  abstract: This important new book sets forth a comprehensive description of various mathematical aspects of problems originating in numerical solution of hyperbolic systems of partial differential equations. The authors present the material in the context of the important mechanical applications of such systems, including the Euler equations of gas dynamics, magnetohydrodynamics (MHD), shallow water, and solid dynamics equations. This treatment provides-for the first time in book form-a collection of recipes for applying higher-order non-oscillatory shock-capturing schemes to MHD modelling of physical phenomena. The authors also address a number of original "nonclassical" problems, such as shock wave propagation in rods and composite materials, ionization fronts in plasma, and electromagnetic shock waves in magnets. They show that if a small-scale, higher-order mathematical model results in oscillations of the discontinuity structure, the variety of admissible discontinuities can exhibit disperse behavior, including some with additional boundary conditions that do not follow from the hyperbolic conservation laws. Nonclassical problems are accompanied by a multiple nonuniqueness of solutions. The authors formulate several selection rules, which in some cases easily allow a correct, physically realizable choice.This work systematizes methods for overcoming the difficulties inherent in the solution of hyperbolic systems. Its unique focus on applications, both traditional and new, makes Mathematical Aspects of Numerical Solution of Hyperbolic Systems particularly valuable not only to those interested the development of numerical methods, but to physicists and engineers who strive to solve increasingly complicated nonlinear equations.
  table of contents: chapter 1 Hyperbolic Systems of Partial Differential Equations -- chapter 2 Numerical Solution of Quasilinear Hyperbolic Systems -- chapter 3 Gas Dynamic Equations -- chapter 4 Shallow Water Equations -- chapter 5 Magnetohydrodynamic Equations -- chapter 6 Solid Dynamics Equations -- chapter 7 Nonclassical Discontinuities and Solutions of Hyperbolic Systems.
  note: by A.G. Kulikovskii, N.V. Pogorelov and A. Yu. Semenov.
  subject:
    topic: MATHEMATICS / Number Systems
  subject:
    topic: MATHEMATICS / Applied
  subject:
    topic: Differential equations, Hyperbolic
    topic: Numerical solutions
  classification: QA377
  classification: 515/.353
  related item:
    title info:
      title: Monographs and surveys in pure and applied mathematics, Chapman & Hall/CRC
  identifier: 9780429175435
  identifier: http://proxy.library.tamu.edu/login
  record info:
    record content source: FlBoTFG
    record creation date: 180611
    record change date: 20220613175734.8
    record identifier: in00004580857