jump to search box

Analysis of finite difference schemes : for linear partial differential equations with generalized solutions / Boško S. Jovanović, Endre Süli.

Availability

Online

At the Library

Other libraries

Author/Creator:
Jovanović, Boško S., author.
Language:
English.
Publication date:
2014
Publication:
London ; New York : Springer, [2014]
Format:
  • Book
  • xiii, 408 pages : illustrations ; 25 cm.
Title Variation:
For linear partial differential equations with generalized solutions
Bibliography:
Includes bibliographical references (pages 389-398) and index.
Contents:
  • Distributions and function spaces
  • Elements of functional analysis
  • A survey of abstract spaces
  • Linear operators in normed linear spaces
  • Sublinear functionals
  • Linear functionals on hilbert spaces
  • Interpolation of banach spaces
  • Basic function spaces
  • Spaces of continuous functions
  • Spaces of integrable functions
  • Distributions
  • Test functions and distributions
  • Operations with distributions
  • Tempered distributions
  • Fourier transform of a tempered distribution
  • Sobolev spaces
  • Anisotropie sobolev spaces
  • Besov spaces
  • Interpolation properties of sobolev spaces
  • Multiplier spaces
  • Fourier multipliers and mollifiers
  • Fourier multipliers
  • Definition of mollifier
  • An admissible class of mollifiers
  • Mollifiers of tempered distributions
  • Multipliers and mollifiers on periodic spaces
  • Elliptic boundary-value problems
  • Existence and uniqueness of solutions
  • Approximation of elliptic problems
  • Introduction to the theory of finite difference schemes
  • Finite difference approximation in one space dimension
  • Finite difference scheme for a univariate problem
  • The multi-dimensional case
  • Approximation of a generalized poisson problem
  • Convergence analysis on uniform meshes
  • The Bramble-Hilbert Lemma
  • Optimal error bounds on uniform meshes
  • Convergence analysis on nonuniform meshes
  • Cartesian-product nonuniform meshes
  • An alternative scheme
  • The rotated discrete laplacian
  • Convergence analysis in Lp norms
  • Discrete fourier multipliers
  • The model problem and its approximation
  • Convergence in discrete bessel-potential norms
  • Approximation of second-order elliptic equations with variable coefficients
  • Convergence in the discrete W¹2 norm
  • Convergence in the discreteW²2 norm
  • Convergence in the discrete L2 norm
  • Convergence in discrete fractional-order norms
  • Convergence in the discrete L2 norm : separated variables
  • Fourth-order elliptic equations
  • An elliptic interface problem
  • Finite difference approximation
  • Convergence in the discrete W¹2 norm
  • Bibliographical notes
  • Finite difference approximation of parabolic problems
  • Parabolicequations
  • Abstract parabolic initial-value problems
  • Some a priori estimates
  • Application to parabolic partial differential equations
  • Abstract two-level operator-difference schemes
  • Classical difference schemes for the heat equation
  • Explicit and implicit schemes
  • Stability of explicit and implicit schemes
  • Error analysis of difference schemes for the heat equation
  • The heatequation with nonsmooth data
  • The initial-boundary-value problem and its discretization
  • Error analysis
  • The case of independent mesh-sizes
  • Parabolic problems with variable coefficients
  • Formulation of the problem
  • The finite difference scheme
  • Error analysis
  • Factorized scheme
  • A parabolic interface problem
  • Finite difference approximation
  • Factorized scheme
  • A parabolic transmission problem
  • Weak solutions and function spaces
  • Finite difference approximation
  • Factorized scheme
  • Bibliographical notes
  • Finite difference approximation of hyperbolic problems
  • Hyperbolic equations
  • Abstract hyperbolic initial-value problems
  • Some a priori estimates
  • Abstract three-level operator-difference schemes
  • Classical difference schemes for the wave equation
  • Explicit and weighted schemes
  • Stability of the weighted difference scheme
  • Error analysis of difference schemes for the wave equation
  • The wave equation with nonsmooth data
  • The initial-boundary-value problem and its discretization
  • Error analysis
  • Hyperbolic problems with variable coefficients
  • Formulation of the problem
  • The finite difference scheme
  • Convergence of the finite difference scheme
  • Factorized scheme
  • Hyperbolic interface problem
  • Finite difference approximation
  • Factorized scheme
  • Hyperbolic transmission problem
  • Finite difference approximation
  • Bibliographical notes
  • References
  • Index
  • List of symbols.
Contributor:
Süli, Endre, 1956- author.
Available in another form:
9781447154600 (online)
(GyWOH)har135025875
Series:
Springer series in computational mathematics, 0179-3632 ; 46
Springer series in computational mathematics ; 46.
Subjects:
ISBN:
9781447154594
1447154592

powered by Blacklight
© Stanford University. Stanford, California 94305. (650) 725-1064. Terms of Use | Copyright Complaints | Opt Out of Analytics
jump to top