Operator theory and numerical methods /

Recent developments in numerical computations are amazing. A lot of huge projects in applied and theoretical sciences are becoming successful by them, while similar things are happening even in the level of personal computers. Under such a situation, theoretical studies on numerical schemes are frui...

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Detalles Bibliográficos
Clasificación:Libro Electrónico
Autores principales: Fujita, Hiroshi, 1928-, Saito, Norikazu (Autor), Suzuki, Takashi (Autor)
Formato: Electrónico eBook
Idioma:Inglés
Publicado: Amsterdam ; London : Elsevier, �2001.
Colección:Studies in mathematics and its applications, v. 30
Temas:
Operator theory.
Numerical analysis.
Th�eorie des op�erateurs.
Analyse num�erique.
Numerical analysis
Operator theory
Operadores (teoria)
An�alise num�erica.
Acceso en línea:Texto completo
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Tabla de Contenidos:
  • 1. Elliptic boundary value problems and FEM ; 1.1 Elliptic boundary value problems
  • 1.2 Ritz-Galerkin method
  • 1.3 Finite element method (FEM)
  • 1.4 Inverse assumption
  • 1.5 L[superscript]infinity [symbol] estimate
  • 1.6 L[superscript]p estimate
  • 1.7 Asymptotic expansion
  • 2. Semigroup theory and FEM ; 2.1 Evolutionary problems
  • 2.2 Semi-discretization
  • 2.3 Fractional powers
  • 2.4 Full-discretization
  • 2.5 Inhomogeneous equation
  • 2.6 Higher accuracy
  • 2.7 L[superscript]infinity [symbol] estimate
  • 2.8 Hyperbolic equation
  • 3. Evolution equations and FEM ; 3.1 Generation theories
  • 3.2 A priori estimates
  • 3.3 Semi-discretization
  • 3.4 Full-discretization
  • 3.5 Alternative approach
  • 4. Other methods in time discretization ; 4.1 Rational approximation of semigroups
  • 4.2 Multi-step method
  • 4.3 Product formula
  • 5. Other methods in space discretization ; 5.1 Lumping of mass
  • 5.2 Upwind finite elements
  • 5.3 Mixed finite elements
  • 5.4 Boundary element method (BEM)
  • 5.5 Charge simulation method (CSM)
  • 6. Nonlinear problems ; 6.1 Semilinear elliptic equations
  • 6.2 Semilinear parabolic equations
  • 6.3 Degenerate parabolic equations
  • 7. Domain decomposition method ; 7.1 Dirichlet to Neumann (DN) map
  • 7.2 Dirichlet to Neumann (DN) iteration
  • 7.3 Dirichlet² to Neumann² (DD-NN) iteration
  • 7.4 Robin to Robin (RR) iteration
  • 7.5 Exterior problem
  • 7.6 The Stokes system.

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