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1.

図書

図書
小泉正二著
出版情報: 東京 : 紀伊國屋書店, 1982.10  iv, 245p ; 22cm
シリーズ名: 紀伊國屋数学叢書 ; 22
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2.

図書

図書
片山孝次著
出版情報: 東京 : 岩波書店, 1982.10  xi, 279p ; 19cm
シリーズ名: 数学入門シリーズ ; 3
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3.

図書

図書
Avner Friedman
出版情報: New York : Wiley, c1982  ix, 710 p. ; 24 cm
シリーズ名: Pure and applied mathematics
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4.

図書

図書
Kerson Huang
出版情報: Singapore : World Scientific, c1982  x, 281 p. ; 24 cm
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5.

図書

図書
Jack Macki, Aaron Strauss
出版情報: New York : Springer-Verlag, c1982  xiii, 165 p. ; 25 cm
シリーズ名: Undergraduate texts in mathematics
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6.

図書

図書
Neal Koblitz, editor
出版情報: Boston : Birkhäuser, 1982  x, 362 p. ; 24 cm
シリーズ名: Progress in mathematics ; vol. 26
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7.

図書

図書
H. Heyer
出版情報: New York : Springer-Verlag, c1982  x, 289 p. ; 25 cm
シリーズ名: Springer series in statistics
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8.

図書

図書
Leon Lapidus, George F. Pinder
出版情報: New York : Wiley, c1982  677 p. ; 24 cm
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目次情報: 続きを見る
Fundamental Concepts / Chapter 1.:
Notation / 1.0.:
First-Order Partial Differential Equations / 1.1.:
First-Order Quasilinear Partial Differential Equations / 1.1.1.:
Initial Value or Cauchy Problem / 1.1.2.:
Application of Characteristic Curves / 1.1.3.:
Nonlinear First-Order Partial Differential Equations / 1.1.4.:
Second-Order Partial Differential Equations / 1.2.:
Linear Second-Order Partial Differential Equations / 1.2.1.:
Classification and Canonical Form of Selected Partial Differential Equations / 1.2.2.:
Quasilinear Partial Differential Equations and Other Ideas / 1.2.3.:
Systems of First-Order PDEs / 1.3.:
First-Order and Second-Order PDEs / 1.3.1.:
Characteristic Curves / 1.3.2.:
Applications of Characteristic Curves / 1.3.3.:
Initial and Boundary Conditions / 1.4.:
References
Basic Concepts in the Finite Difference and Finite Element Methods / Chapter 2.:
Introduction / 2.0.:
Finite Difference Approximations / 2.1.:
Taylor Series Expansions / 2.1.1.:
Operator Notation for u(x) / 2.1.3.:
Finite Difference Approximations in Two Dimensions / 2.1.4.:
Additional Concepts / 2.1.5.:
Introduction to Finite Element Approximations / 2.2.:
Method of Weighted Residuals / 2.2.1.:
Application of the Method of Weighted Residuals / 2.2.2.:
The Choice of Basis Functions / 2.2.3.:
Two-Dimensional Basis Functions / 2.2.4.:
Approximating Equations / 2.2.5.:
Relationship between Finite Element and Finite Difference Methods / 2.3.:
Finite Elements on Irregular Subspaces / Chapter 3.:
Triangular Elements / 3.0.:
The Linear Triangular Element / 3.1.1.:
Area Coordinates / 3.1.2.:
The Quadratic Triangular Element / 3.1.3.:
The Cubic Triangular Element / 3.1.4.:
Higher-Order Triangular Elements / 3.1.5.:
Isoparametric Finite Elements / 3.2.:
Transformation Functions / 3.2.1.:
Numerical Integration / 3.2.2.:
Isoparametric Serendipity Hermitian Elements / 3.2.3.:
Isoparametric Hermitian Elements in Normal and Tangential Coordinates / 3.2.4.:
Boundary Conditions / 3.3.:
Three-Dimensional Elements / 3.4.:
Parabolic Partial Differential Equations / Chapter 4.:
Partial Differential Equations / 4.0.:
Well-Posed Partial Differential Equations / 4.1.1.:
Model Difference Approximations / 4.2.:
Well-Posed Difference Forms / 4.2.1.:
Derivation of Finite Difference Approximations / 4.3.:
The Classic Explicit Approximation / 4.3.1.:
The Dufort-Frankel Explicit Approximation / 4.3.2.:
The Richardson Explicit Approximation / 4.3.3.:
The Backwards Implicit Approximation / 4.3.4.:
The Crank-Nicolson Implicit Approximation / 4.3.5.:
The Variable-Weighted Implicit Approximation / 4.3.6.:
Consistency and Convergence / 4.4.:
Stability / 4.5.:
Heuristic Stability / 4.5.1.:
Von Neumann Stability / 4.5.2.:
Matrix Stability / 4.5.3.:
Some Extensions / 4.6.:
Influence of Lower-Order Terms / 4.6.1.:
Higher-Order Forms / 4.6.2.:
Predictor-Corrector Methods / 4.6.3.:
Asymmetric Approximations / 4.6.4.:
Variable Coefficients / 4.6.5.:
Nonlinear Parabolic PDEs / 4.6.6.:
The Box Method / 4.6.7.:
Solution of Finite Difference Approximations / 4.7.:
Solution of Implicit Approximations / 4.7.1.:
Explicit versus Implicit Approximations / 4.7.2.:
Composite Solutions / 4.8.:
Global Extrapolation / 4.8.1.:
Some Numerical Results / 4.8.2.:
Local Combination / 4.8.3.:
Composites of Different Approximations / 4.8.4.:
Finite Difference Approximations in Two Space Dimensions / 4.9.:
Explicit Methods / 4.9.1.:
Irregular Boundaries / 4.9.2.:
Implicit Methods / 4.9.3.:
Alternating Direction Explicit (ADE) Methods / 4.9.4.:
Alternating Direction Implicit (ADI) Methods / 4.9.5.:
LOD and Fractional Splitting Methods / 4.9.6.:
Hopscotch Methods / 4.9.7.:
Mesh Refinement / 4.9.8.:
Three-Dimensional Problems / 4.10.:
ADI Methods / 4.10.1.:
Iterative Solutions / 4.10.2.:
Finite Element Solution of Parabolic Partial Differential Equations / 4.11.:
Galerkin Approximation to the Model Parabolic Partial Differential Equation / 4.11.1.:
Approximation of the Time Derivative / 4.11.2.:
Approximation of the Time Derivative for Weakly Nonlinear Equations / 4.11.3.:
Finite Element Approximations in One Space Dimension / 4.12.:
Formulation of the Galerkin Approximating Equations / 4.12.1.:
Linear Basis Function Approximation / 4.12.2.:
Higher-Degree Polynomial Basis Function Approximation / 4.12.3.:
Formulation Using the Dirac Delta Function / 4.12.4.:
Orthogonal Collocation Formulation / 4.12.5.:
Asymmetric Weighting Functions / 4.12.6.:
Finite Element Approximations in Two Space Dimensions / 4.13.:
Galerkin Approximation in Space and Time / 4.13.1.:
Galerkin Approximation in Space Finite Difference in Time / 4.13.2.:
Asymmetric Weighting Functions in Two Space Dimensions / 4.13.3.:
Lumped and Consistent Time Matrices / 4.13.4.:
Collocation Finite Element Formulation / 4.13.5.:
Treatment of Sources and Sinks / 4.13.6.:
Alternating Direction Formulation / 4.13.7.:
Finite Element Approximations in Three Space Dimensions / 4.14.:
Example Problem / 4.14.1.:
Summary / 4.15.:
Elliptic Partial Differential Equations / Chapter 5.:
Model Elliptic PDEs / 5.0.:
Specific Elliptic PDEs / 5.1.1.:
Further Items / 5.1.2.:
Finite Difference Solutions in Two Space Dimensions / 5.2.:
Five-Point Approximations and Truncation Error / 5.2.1.:
Nine-Point Approximations and Truncation Error / 5.2.2.:
Approximations to the Biharmonic Equation / 5.2.3.:
Boundary Condition Approximations / 5.2.4.:
Matrix Form of Finite Difference Equations / 5.2.5.:
Direct Methods of Solution / 5.2.6.:
Iterative Concepts / 5.2.7.:
Formulation of Point Iterative Methods / 5.2.8.:
Convergence of Point Iterative Methods / 5.2.9.:
Line and Block Iteration Methods / 5.2.10.:
Acceleration and Semi-Iterative Overlays / 5.2.11.:
Finite Difference Solutions in Three Space Dimensions / 5.3.:
Iteration Concepts / 5.3.1.:
Finite Element Methods for Two Space Dimensions / 5.3.3.:
Galerkin Approximation / 5.4.1.:
Collocation Approximation / 5.4.2.:
Mixed Finite Element Approximation / 5.4.4.:
Approximation of the Biharmonic Equation / 5.4.5.:
Boundary Integral Equation Methods / 5.5.:
Fundamental Theory / 5.5.1.:
Boundary Element Formulation / 5.5.2.:
Linear Interpolation Functions / 5.5.3.:
Poisson's Equation / 5.5.5.:
Nonhomogeneous Materials / 5.5.6.:
Combination of Finite Element and Boundary Integral Equation Methods / 5.5.7.:
Three-Dimensional Finite Element Simulation / 5.6.:
Hyperbolic Partial Differential Equations / 5.7.:
Equations of Hyperbolic Type / 6.0.:
Finite Difference Solution of First-Order Scalar Hyperbolic Partial Differential Equations / 6.2.:
Stability, Truncation Error, and Other Features / 6.2.1.:
Other Approximations / 6.2.2.:
Dissipation and Dispersion / 6.2.3.:
Hopscotch Methods and Mesh Refinement / 6.2.4.:
Finite Difference Solution of First-Order Vector Hyperbolic Partial Differential Equations / 6.3.:
Finite Difference Solution of First-Order Vector Conservative Hyperbolic Partial Differential Equations / 6.4.:
Finite Difference Solutions to Two- and Three-Dimensional Hyperbolic Partial Differential Equations / 6.5.:
Finite Difference Schemes / 6.5.1.:
Two-Step, ADI, and Strang-Type Algorithms / 6.5.2.:
Conservative Hyperbolic Partial Differential Equations / 6.5.3.:
Finite Difference Solution of Second-Order Model Hyperbolic Partial Differential Equations / 6.6.:
One-Space-Dimension Hyperbolic Partial Differential Equation / 6.6.1.:
Explicit Algorithms / 6.6.2.:
Implicit Algorithms / 6.6.3.:
Simultaneous First-Order Partial Differential Equations / 6.6.4.:
Mixed Systems / 6.6.5.:
Two- and Three-Space-Dimensional Hyperbolic Partial Differential Equations / 6.6.6.:
Implicit ADI and LOD Methods / 6.6.7.:
Finite Element Solution of First-Order Model Hyperbolic Partial Differential Equations / 6.7.:
Asymmetric Weighting Function Approximation / 6.7.1.:
An H[superscript -1] Galerkin Approximation / 6.7.3.:
Orthogonal Collocation with Asymmetric Bases / 6.7.4.:
Finite Element Solution of Two- and Three-Space-Dimensional First-Order Hyperbolic Partial Differential Equations / 6.7.6.:
Galerkin Finite Element Formulation / 6.8.1.:
Finite Element Solution of First-Order Vector Hyperbolic Partial Differential Equations / 6.8.2.:
Finite Element Solution of Two- and Three-Space-Dimensional First-Order Vector Hyperbolic Partial Differential Equations / 6.9.1.:
Finite Element Solution of One-Space-Dimensional Second-Order Hyperbolic Partial Differential Equations / 6.10.1.:
Time Approximations / 6.11.1.:
Finite Element Solution of Two- and Three-Space-Dimensional Second-Order Hyperbolic Partial Differential Equations / 6.11.3.:
Index / 6.12.1.:
Fundamental Concepts / Chapter 1.:
Notation / 1.0.:
First-Order Partial Differential Equations / 1.1.:
9.

図書

図書
prepared for the International Statistical Institute by Maurice G. Kendall & William R. Buckland
出版情報: London ; New York : Published for the International Statistical Institute by Longman, 1982  213 p. ; 25 cm
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10.

図書

図書
Shui-Nee Chow, Jack K. Hale
出版情報: New York ; Berlin : Springer-Verlag, c1982  xv, 515 p. ; 25 cm
シリーズ名: Die Grundlehren der mathematischen Wissenschaften ; 251
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