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1.

図書

図書
Joel H. Ferziger
出版情報: New York : Wiley, c1981  xii, 270 p. ; 25 cm
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2.

図書

図書
P.K. Banerjee and R. Butterfield
出版情報: London ; Tokyo : McGraw-Hill, c1981  xiv, 452 p. ; 23 cm
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3.

図書

図書
editors, M. Tanaka, C.A. Brebbia
出版情報: Southampton : Computational Mechanics Institute , Berlin ; Tokyo : Springer-Verlag, c1986  2 v. (xix, 917 p.) ; 24 cm
シリーズ名: A Computational mechanics publication
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4.

図書

図書
Jayme Mason
出版情報: Amsterdam ; New York : Elsevier Scientific Pub. Co , New York : Distributors for the U.S. and Canada, Elsevier/North-Holland, 1980  xiv, 368 p. ; 25 cm
シリーズ名: Studies in applied mechanics ; 4
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5.

図書

図書
Joel H. Ferziger
出版情報: New York : Wiley, c1998  xvii, 378 p. ; 25 cm
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6.

図書

図書
Bilal M. Ayyub, Richard H. McCuen
出版情報: Boca Raton : CRC Press, c1997  514 p. ; 24 cm
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7.

図書

図書
edited by Jewgeni H. Dshalalow
出版情報: Boca Raton, Fla. : CRC Press, c1997  468 p. ; 26 cm
シリーズ名: Probability and stochastics series
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8.

図書

図書
Brian H. Chirgwin and Charles Plumpton
出版情報: New York ; Oxford : Pergamon Press, 1961-1964  v. ; 22 cm
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9.

図書

図書
editor, C.A. Brebbia
出版情報: Southampton : Computational Mechanics Centre Publication , Berlin ; Tokyo : Springer-Verlag, c1984  1 v. (various pagings) ; 24 cm
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10.

図書

図書
editors, C.A. Brebbia, G. Maier
出版情報: [Southampton] : Wessex Institute of Technology , Berlin ; Tokyo : Springer-Verlag, c1985  2 v. ; 24 cm
シリーズ名: A Computational mechanics publication
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11.

図書

図書
A. C. Bajpai, L. R. Mustoe, D. Walker
出版情報: Cichester [Eng.] : J. Wiley, c1980  ix, 401 p. ; 24 cm
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12.

図書

図書
by Alfred J. Menezes, editor ; Ian F. Blake ... [et al.]
出版情報: Boston : Kluwer Academic Publishers, c1993  xi, 218 p. ; 24 cm
シリーズ名: The Kluwer international series in engineering and computer science ; SECS 199 . Communications and information theory
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13.

図書

図書
Roger G. Ghanem, Pol D. Spanos
出版情報: New York ; Tokyo : Springer-Verlag, c1991  x, 214 p. ; 24 cm
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14.

図書

図書
Houston N. Irvine
出版情報: New York : M. Dekker, c1981  vii, 239 p. ; 23 cm
シリーズ名: Engineering technology ; 2
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15.

図書

図書
A. Wayne Wymore
出版情報: New York : Wiley, c1967  xii, 353 p. ; 24 cm
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16.

図書

図書
Thomas M. Creese, Robert M. Haralick
出版情報: New York : McGraw-Hill, c1978  xvi, 552 p. ; 25 cm
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17.

図書

図書
T.T. Furman
出版情報: London ; New York : Academic Press, 1981  viii, 388 p. ; 24 cm
シリーズ名: Mathematics in science and engineering : a series of monographs and textbooks ; v. 155
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18.

図書

図書
editor, C.A. Brebbia
出版情報: Southampton : Computational Mechanics , Berlin ; Tokyo : Springer-Verlag, c1988  641 p. ; 24 cm
シリーズ名: Boundary elements X ; v. 1
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19.

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.:
20.

図書

図書
Ralph J. Harker
出版情報: New York : Wiley, c1983  xxii, 435 p. ; 25 cm
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21.

図書

図書
John W. Dettman
出版情報: New York : McGraw-Hill, 1962  xii, 323 p. ; 24 cm
シリーズ名: International series in pure and applied mathematics
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22.

図書

図書
editors, C. A. Brebbia, T. Futagami, M. Tanaka
出版情報: Southampton : Computational Mechanics Centre, 1983  1046 p. ; 24 cm
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23.

図書

図書
Jacques Dupraz ; translated by A. Howie
出版情報: London : North Oxford Academic, 1986  xiii, 344 p. ; 24cm
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24.

図書

図書
A. Wayne Wymore
出版情報: Boca Raton : CRC Press, c1993  xiii, 710 p. ; 25 cm
シリーズ名: Systems engineering series
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25.

図書

図書
C.A. Brebbia, J.C.F. Telles, L.C. Wrobel
出版情報: Berlin ; Tokyo : Springer-Verlag, 1984  xiv, 464 p. ; 26 cm
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26.

図書

図書
I.S. Sokolnikoff, R.M. Redheffer
出版情報: Singapore ; Tokyo : McGraw-Hill International Book Co., 1966  xi, 752 p. ; 25 cm
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27.

図書

図書
R.S. Schechter
出版情報: New York : McGraw-Hill, c1967  [vii], 287 p. ; 23 cm
シリーズ名: McGraw-Hill chemical engineering series
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28.

図書

図書
Néstor Distéfano
出版情報: New York : Academic Press, 1974  xvii, 366 p. ; 24 cm
シリーズ名: Mathematics in science and engineering : a series of monographs and textbooks ; v. 110
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29.

図書

図書
edited by Carlos A. Brebbia
出版情報: Ashurst, Southampton : Computational Mechanics, 1985  97p ; 28cm
シリーズ名: Progress in engineering sciences
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30.

図書

図書
Parviz Moin
出版情報: Cambridge : Cambridge University Press, 2010  xiv, 241 p. ; 26 cm
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目次情報: 続きを見る
Preface to the Second Edition
Preface to the First Edition
Interpolation / 1:
Lagrange Polynomial Interpolation / 1.1:
Cubic Spline Interpolation / 1.2:
Exercises
Further Reading
Numerical Differentiation - Finite Differences / 2:
Construction of Difference Formulas Using Taylor Series / 2.1:
A General Technique for Construction of Finite Difference Schemes / 2.2:
An Alternative Measure for the Accuracy of Finite Differences / 2.3:
Padé Approximations / 2.4:
Non-Uniform Grids / 2.5:
Numerical Integration / 3:
Trapezoidal and Simpson's Rules / 3.1:
Error Analysis / 3.2:
Trapezoidal Rule with End-Correction / 3.3:
Romberg Integration and Richardson Extrapolation / 3.4:
Adaptive Quadrature / 3.5:
Gauss Quadrature / 3.6:
Numerical Solution of Ordinary Differential Equations / 4:
Initial Value Problems / 4.1:
Numerical Stability / 4.2:
Stability Analysis for the Euler Method / 4.3:
Implicit or Backward Euler / 4.4:
Numerical Accuracy Revisited / 4.5:
Trapezoidal Method / 4.6:
Linearization for Implicit Methods / 4.7:
Runge-Kutta Methods / 4.8:
Multi-Step Methods / 4.9:
System of First-Order Ordinary Differential Equations / 4.10:
Boundary Value Problems / 4.11:
Shooting Method / 4.11.1:
Direct Methods / 4.11.2:
Numerical Solution of Partial Differential Equations / 5:
Semi-Discretization / 5.1:
von Neumann Stability Analysis / 5.2:
Modified Wavenumber Analysis / 5.3:
Implicit Time Advancement / 5.4:
Accuracy via Modified Equation / 5.5:
Du Fort-Frankel Method: An Inconsistent Scheme / 5.6:
Multi-Dimensions / 5.7:
Implicit Methods in Higher Dimensions / 5.8:
Approximate Factorization / 5.9:
Stability of the Factored Scheme / 5.9.1:
Alternating Direction Implicit Methods / 5.9.2:
Mixed and Fractional Step Methods / 5.9.3:
Elliptic Partial Differential Equations / 5.10:
Iterative Solution Methods / 5.10.1:
The Point Jacobi Method / 5.10.2:
Gauss-Seidel Method / 5.10.3:
Successive Over Relaxation Scheme / 5.10.4:
Multigrid Acceleration / 5.10.5:
Discrete Transform Methods / 6:
Fourier Series / 6.1:
Discrete Fourier Series / 6.1.1:
Fast Fourier Transform / 6.1.2:
Fourier Transform of a Real Function / 6.1.3:
Discrete Fourier Series in Higher Dimensions / 6.1.4:
Discrete Fourier Transform of a Product of Two Functions / 6.1.5:
Discrete Sine and Cosine Transforms / 6.1.6:
Applications of Discrete Fourier Series / 6.2:
Direct Solution of Finite Differenced Elliptic Equations / 6.2.1:
Differentiation of a Periodic Function Using Fourier Spectral Method / 6.2.2:
Numerical Solution of Linear, Constant Coefficient Differential Equations with Periodic Boundary Conditions / 6.2.3:
Matrix Operator for Fourier Spectral Numerical Differentiation / 6.3:
Discrete Chebyshev Transform and Applications / 6.4:
Numerical Differentiation Using Chebyshev Polynomials / 6.4.1:
Quadrature Using Chebyshev Polynomials / 6.4.2:
Matrix Form of Chebyshev Collocation Derivative / 6.4.3:
Method of Weighted Residuals / 6.5:
The Finite Element Method / 6.6:
Application of the Finite Element Method to a Boundary Value Problem / 6.6.1:
Comparison with Finite Difference Method / 6.6.2:
Comparison with a Padé Scheme / 6.6.3:
A Time-Dependent Problem / 6.6.4:
Application to Complex Domains / 6.7:
Constructing the Basis Functions / 6.7.1:
A Review of Linear Algebra / A:
Vectors, Matrices and Elementary Operations / A.1:
System of Linear Algebraic Equations / A.2:
Effects of Round-off Error / A.2.1:
Operations Counts / A.3:
Eigenvalues and Eigenvectors / A.4:
Index
Preface to the Second Edition
Preface to the First Edition
Interpolation / 1:
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