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QA377 .J684 2014
Nonlinear methods in Riemannian and...
1991
Jost, Jürgen, 1956
Math & Statistics Library » QA377 .J67 1991
Journal of hyperbolic differential ...
2004
SAL3 (offcampus storage) » QA377 .J68 V.1:NOS.34 2004
Analysis of finite difference schemes
2014
Jovanović, Boško S.
Math & Statistics Library » QA377 .J684 2014
Multiple scattering processes
1975
Natsuyama, H. H. (Harriet H.), 1937
Math & Statistics Library » QA377 .K33
Statistical and computational inver...
2005
Kaipio, Jari
Math & Statistics Library » QA377 .K34 2005
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Analysis of finite difference schemes : for linear partial differential equations with generalized solutions / Boško S. Jovanović, Endre Süli.
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QA377 .J684 2014
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QA377 .J684 2014
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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 389398) 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 boundaryvalue 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 multidimensional case
Approximation of a generalized poisson problem
Convergence analysis on uniform meshes
The BrambleHilbert Lemma
Optimal error bounds on uniform meshes
Convergence analysis on nonuniform meshes
Cartesianproduct 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 besselpotential norms
Approximation of secondorder 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 fractionalorder norms
Convergence in the discrete L2 norm : separated variables
Fourthorder 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 initialvalue problems
Some a priori estimates
Application to parabolic partial differential equations
Abstract twolevel operatordifference 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 initialboundaryvalue problem and its discretization
Error analysis
The case of independent meshsizes
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 initialvalue problems
Some a priori estimates
Abstract threelevel operatordifference 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 initialboundaryvalue 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, 01793632 ; 46
Springer series in computational mathematics ;
46.
Subjects:
Boundary value problems.
Differential equations, Partial
>
Numerical solutions.
Finite volume method.
Finite differences.
Numerical analysis.
ISBN:
9781447154594
1447154592
Catkey: 10317685
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