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1.

図書

図書
Ernst Hairer, Christian Lubich, Gerhard Wanner
出版情報: Berlin ; Tokyo : Springer, c2002  xiii, 515 p. ; 24 cm
シリーズ名: Springer series in computational mathematics ; v. 31
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2.

図書

図書
Y. Eliashberg, N. Mishachev
出版情報: Providence, R.I. : American Mathematical Society, c2002  xvii, 206 p. ; 26 cm
シリーズ名: Graduate studies in mathematics ; v. 48
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目次情報: 続きを見る
Intrigue Holonomic approximation: Jets and holonomy
Thom transversality theorem Holonomic approximation
Applications Differential relations and Gromov's $h$-principle: Differential relations
Homotopy principle Open Diff $V$-invariant differential relations
Applications to closed manifolds
The homotopy principle in symplectic geometry: Symplectic and contact basics
Symplectic and contact structures on open manifolds
Symplectic and contact structures on closed manifolds
Embeddings into symplectic and contact manifolds
Microflexibility and holonomic $\mathcal{R}$-approximation
First applications of microflexibility
Microflexible $\mathfrak{U}$-invariant differential relations
Further applications to symplectic geometry
Convex integration: One-dimensional convex integration
Homotopy principle for ample differential relations
Directed immersions and embeddings
First order linear differential operators Nash-Kuiper theorem
Bibliography
Index
Intrigue Holonomic approximation: Jets and holonomy
Thom transversality theorem Holonomic approximation
Applications Differential relations and Gromov's $h$-principle: Differential relations
3.

図書

図書
Franz J. Vesely
出版情報: New York : Kluwer Academic/Plenum Publishers, c2001  xvi, 259 p. ; 26 cm
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目次情報: 続きを見る
The Three Pillars of Computational Physics / I:
Finite Differences / 1:
Interpolation Formulae / 1.1:
NGF Interpolation / 1.1.1:
NGB Interpolation / 1.1.2:
ST Interpolation / 1.1.3:
Difference Quotients / 1.2:
DNGF Formulae / 1.2.1:
DNGB Formulae / 1.2.2:
DST Formulae / 1.2.3:
Finite Differences in Two Dimensions / 1.3:
Sample Applications / 1.4:
Classical Point Mechanics / 1.4.1:
Diffusion and Thermal Conduction / 1.4.2:
Linear Algebra / 2:
Exact Methods / 2.1:
Gauss Elimination and Back Substitution / 2.1.1:
Simplifying Matrices: The Householder Transformation / 2.1.2:
LU Decomposition / 2.1.3:
Tridiagonal Matrices: Recursion Method / 2.1.4:
Iterative Methods / 2.2:
Jacobi Relaxation / 2.2.1:
Gauss-Seidel Relaxation (GSR) / 2.2.2:
Successive Over-Relaxation (SOR) / 2.2.3:
Alternating Direction Implicit Method (ADI) / 2.2.4:
Conjugate Gradient Method (CG) / 2.2.5:
Eigenvalues and Eigenvectors / 2.3:
Largest Eigenvalue and Related Eigenvector / 2.3.1:
Arbitrary Eigenvalue/-vector: Inverse Iteration / 2.3.2:
Potential Equation / 2.4:
Electronic Orbitals / 2.4.3:
Stochastics / 3:
Equidistributed Random Variates / 3.1:
Linear Congruential Generators / 3.1.1:
Shift Register Generators / 3.1.2:
Other Distributions / 3.2:
Fundamentals / 3.2.1:
Transformation Method / 3.2.2:
Generalized Transformation Method / 3.2.3:
Rejection Method / 3.2.4:
Multivariate Gaussian Distribution / 3.2.5:
Equidistribution in Orientation Space / 3.2.6:
Random Sequences / 3.3:
Markov Processes / 3.3.1:
Autoregressive Processes / 3.3.3:
Wiener-Levy Process / 3.3.4:
Markov Chains and the Monte Carlo method / 3.3.5:
Stochastic Optimization / 3.4:
Simulated Annealing / 3.4.1:
Genetic Algorithms / 3.4.2:
Everything Flows / II:
Ordinary Differential Equations / 4:
Initial Value Problems of First Order / 4.1:
Euler-Cauchy Algorithm / 4.1.1:
Stability and Accuracy of Difference Schemes / 4.1.2:
Explicit Methods / 4.1.3:
Implicit Methods / 4.1.4:
Predictor-Corrector Method / 4.1.5:
Runge-Kutta Method / 4.1.6:
Extrapolation Method / 4.1.7:
Initial Value Problems of Second Order / 4.2:
Verlet Method / 4.2.1:
Nordsieck Formulation of the PC Method / 4.2.2:
Symplectic Algorithms / 4.2.4:
Numerov's Method / 4.2.6:
Boundary Value Problems / 4.3:
Shooting Method / 4.3.1:
Relaxation Method / 4.3.2:
Partial Differential Equations / 5:
Initial Value Problems I (Hyperbolic) / 5.1:
FTCS Scheme; Stability Analysis / 5.1.1:
Lax Scheme / 5.1.2:
Leapfrog Scheme (LF) / 5.1.3:
Lax-Wendroff Scheme (LW) / 5.1.4:
Lax and Lax-Wendroff in Two Dimensions / 5.1.5:
Initial Value Problems II (Parabolic) / 5.2:
FTCS Scheme / 5.2.1:
Implicit Scheme of First Order / 5.2.2:
Crank-Nicholson Scheme (CN) / 5.2.3:
Dufort-Frankel Scheme (DF) / 5.2.4:
Boundary Value Problems: Elliptic DE / 5.3:
Relaxation and Multigrid Techniques / 5.3.1:
ADI Method for the Potential Equation / 5.3.2:
Fourier Transform Method (FT) / 5.3.3:
Cyclic Reduction (CR) / 5.3.4:
Anchors Aweigh / III:
Simulation and Statistical Mechanics / 6:
Model Systems of Statistical Mechanics / 6.1:
A Nutshellfull of Fluids and Solids / 6.1.1:
Tricks of the Trade / 6.1.2:
Monte Carlo Method / 6.2:
Molecular Dynamics Simulation / 6.3:
Hard Spheres / 6.3.1:
Continuous Potentials / 6.3.2:
Beyond Basic Molecular Dynamics / 6.3.3:
Evaluation of Simulation Experiments / 6.4:
Pair Correlation Function / 6.4.1:
Autocorrelation Functions / 6.4.2:
Particles and Fields / 6.5:
Ewald summation / 6.5.1:
Particle-Mesh Methods (PM and P3M) / 6.5.2:
Stochastic Dynamics / 6.6:
Quantum Mechanical Simulation / 7:
Diffusion Monte Carlo (DMC) / 7.1:
Path Integral Monte Carlo (PIMC) / 7.2:
Wave Packet Dynamics (WPD) / 7.3:
Density Functional Molecular Dynamics (DFMD) / 7.4:
Hydrodynamics / 8:
Compressible Flow without Viscosity / 8.1:
Explicit Eulerian Methods / 8.1.1:
Particle-in-Cell Method (PIC) / 8.1.2:
Smoothed Particle Hydrodynamics (SPH) / 8.1.3:
Incompressible Flow with Viscosity / 8.2:
Vorticity Method / 8.2.1:
Pressure Method / 8.2.2:
Free Surfaces: Marker-and-Cell Method (MAC) / 8.2.3:
Lattice Gas Models for Hydrodynamics / 8.3:
Lattice Gas Cellular Automata / 8.3.1:
The Lattice Boltzmann Method / 8.3.2:
Direct Simulation Monte Carlo / Bird method / 8.4:
Appendixes
Machine Errors / A:
Discrete Fourier Transformation / B:
Fast Fourier Transform (FFT) / B.1:
Bibliography
Index
The Three Pillars of Computational Physics / I:
Finite Differences / 1:
Interpolation Formulae / 1.1:
4.

図書

図書
by Maria do Rosário Grossinho and Stepan Agop Tersian
出版情報: Dordrecht : Kluwer Academic Publishers, c2001  xii, 269 p. ; 25 cm
シリーズ名: Nonconvex optimization and its applications ; v. 52
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5.

図書

図書
William Edmund Milne
出版情報: New York : Wiley, c1953  xi, 275 p. ; 24 cm
シリーズ名: Applied mathematics series
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6.

図書

図書
Nail H. Ibragimov
出版情報: Chichester, West Sussex ; New York : Wiley, c1999  xviii, 347 p. ; 24 cm
シリーズ名: Mathematical methods in practice ; v. 4
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目次情報: 続きを見る
Introduction to Differential Equations
Transformation Groups
Lie Group Analysis of Ordinary Differential Equations
Brief on Lie Algebras
First Order Differential Equations
Integration of Second Order Equations
Basic Theory of Linear Equations
Nonlinear Second Order Equations
Integration of Third Order Equations
Nonlinear Superposition Principle
Index
Introduction to Differential Equations
Transformation Groups
Lie Group Analysis of Ordinary Differential Equations
7.

図書

図書
edited by S.M. Rao
出版情報: San Diego ; Tokyo : Academic Press, 1999  xi, 372 p. ; 26 cm
シリーズ名: Academic Press series in engineering
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目次情報: 続きを見る
Preface
Acknowledgments
Contributors
Introduction / Miller1.:
An Initial Exploration of Time Domain Phenomena / 1.1:
The Infinite-Length Wire Antenna / 1.1.1:
The Finite-Length Wire Antenna / 1.1.2:
The Finite-Length Wire Scatterer / 1.1.3:
Late-Time Radiation from an Impulsively Excited Perfect Conductor / 1.1.4:
Some Special Capabilities of Time Domain Models / 1.1.5:
Modeling Chocies in CEM / 1.2:
Why Model in the Time Domain? / 1.2.1:
Evolution of Time Domain Modeling / 1.2.2:
Some General References / 1.2.3:
General Aspects of Time Domain Modeling / 1.3:
Model Development / 1.3.1:
Explicit vs Implicit Solution / 1.3.2:
Excitation Requirements / 1.3.3:
TD Solution / 1.3.4:
Time Domain Integral Equation Modeling / 1.4:
Some Representative TDIEs / 1.4.1:
A Prototype TDIE Model / 1.4.2:
Alternate Forms for a TDIE Solution / 1.4.3:
Excitation of a TDIE Model / 1.4.4:
Physical Implication of a TDIE Explicit Model / 1.4.5:
A Near-Neighbor TD Approximation / 1.4.6:
Time Domain Differential Equation Modeling / 1.5:
Space-Time Sampling of TDDE / 1.5.1:
Some Spatial-Mesh Alternatives / 1.5.2:
Mesh Closure Conditions / 1.5.3:
Handling Small Features in DE Models / 1.5.4:
Obtaining Far Fields from DE Models / 1.5.5:
Variations of TDDE Models / 1.5.6:
Comparison of TDDE and TDIE Models / 1.5.7:
Specific Issues Related to Time Domain Modeling / 1.6:
Increasing the Stability of the Time-Stepping Solution / 1.6.1:
Exploiting EM Singularities / 1.6.2:
Signal Processing as a Part of TD Modeling / 1.6.3:
Total-Field and Scattered-Field Formulations / 1.6.4:
Handling Frequency Dispersion and Loading in TD Models / 1.6.5:
Handling Medium and Component Nonlinearities or Time Variations in TD Models / 1.6.6:
Hybrid TD Models / 1.6.7:
The Concept of Pseudo-Time in Iterative FD Solutions / 1.6.8:
Exploiting Symmetries in TD Modeling / 1.6.9:
Concluding Remarks / 1.7:
Bibliography
Wire Structures: TDIE Solution / Rao ; Sarkar2.:
Basic Analysis / 2.1:
Analysis of a Straight Wire / 2.2:
Method of Moments Solution / 2.2.1:
Conjugate Gradient Method Solution / 2.2.2:
Numerical Example / 2.2.3:
Analysis of an Arbitrary Wire / 2.3:
Moment Method Solution / 2.3.1:
Conjugate Gradient Method / 2.3.2:
Numerical Examples / 2.3.3:
Implicit Solution Scheme / 2.4:
Application to Arbitrary Wire / 2.4.1:
Numerical Implementation / 2.4.2:
Analysis of Multiple Wires and Wire Junctions / 2.4.3:
Infinite Conducting Cylinders: TDIE Solution / Vechinski2.6:
Integral Equation Formulation / 3.1:
Discretization Scheme / 3.2:
TM Incidence: EFIE Formulation / 3.3:
Explicit Solution Procedure / 3.3.1:
Implicit Solution Procedure / 3.3.2:
TE Incidence: EFIE Formulation / 3.3.3:
TE Incidence: HFIE Formulation / 3.4.1:
Finite Conducting Bodies: TDIE Solution / 3.5.1:
Numerical Solution Scheme / 4.1:
Explicit Numerical Method / 4.2.1:
Implicit Numerical Method / 4.2.2:
Efficiency Considerations / 4.2.3:
Far-Scattered Fields / 4.2.4:
Near-Scattered Fields / 4.3.1:
Extrapolation of Time Domain Response / 4.5:
Matrix Pencil Method / 4.5.1:
Total Least Squares Matrix Pencil / 4.5.2:
Dielectric Bodies: TDIE Solution / 4.5.3:
Two-Dimensional Cylinders / 5.1:
Numerical Solution Procedure / 5.2.1:
Three-Dimensional Bodies / 5.2.2:
Finite-Difference Time Domain Method / Umashankar5.3.1:
Introduction to FDTD / 6.1:
Pulse Propagation in a Lossy, Inhomogeneous, Layered Medium / 6.2:
Propagation of Half-Sine Pulse / 6.2.1:
Remote Sensing of Inhomogeneous, Lossy, Layered Media / 6.3:
Profile Inversion Results / 6.3.1:
Key Elements of FDTD Modeling Theory / 6.4:
FDTD Formulation for Two-Dimensional Closed-Region Problems / 6.5:
FDTD Formulation for TM and TE Cases / 6.5.1:
Hollow Rectangular Waveguide / 6.5.2:
Dielectric Slab-Loaded Rectangular Waveguide / 6.5.3:
Shielded Microstrip Lines / 6.5.4:
FDTD Formulation for Two-Dimensional Open-Region Problems / 6.6:
Absorbing Radiation Boundary Condition / 6.6.1:
Second-Order Radiation Boundary Condition / 6.6.2:
Plane Wave Source Condition / 6.7:
Near- to Far-Field Transformation / 6.8:
FDTD Modeling of Curved Surfaces / 6.9:
Perfectly Conducting Object: The TE Case / 6.9.1:
Perfectly Conducting Object: The TM Case / 6.9.2:
Homogeneous Dielectric Object: The TE Case / 6.9.3:
FDTD Formulation for Three-Dimensional Closed-Region Problems / 6.10:
Three-Dimensional Full-Wave Analysis / 6.10.1:
Compact Two-Dimensional FDTD Algorithm / 6.10.2:
Evaluation of Dispersion Characteristics / 6.10.3:
FDTD Formulation for Three-Dimensional Open-Region Problems / 6.11:
Three-Dimensional Plane Wave Source Condition / 6.11.1:
Near- to Far-Field Transformation for the Three-Dimensional Case / 6.12:
RCS of a Flat-Plate Scatterer / 6.12.1:
Computer Resources and Modeling Implications / 6.13:
Transmission Line Modeling Method / Gothard ; German6.14:
The Two-Dimensional TLM / 7.1:
Time Domain Wave Equation / 7.1.1:
Time Domain Transmission Line Equation / 7.1.2:
Equating Maxwell's and the Circuit Equations / 7.1.3:
General Scattering Matrix Theory / 7.1.4:
Applying Scattering Theory to the Free-Space Shunt T-Line / 7.1.5:
Modeling Inhomogeneous Lossy Media / 7.1.6:
Excitation of the TLM Mesh and Metallic Boundaries / 7.1.7:
TLM Mesh Truncation Conditions / 7.1.8:
Discretization of the TLM Spatial Grid / 7.1.9:
TLM Output / 7.1.10:
The Series Node and Duality / 7.1.11:
Outline of the Algorithm for Two-Dimensional TLM Code / 7.1.12:
Three-Dimensional TLM / 7.2:
Special Features in TLM / 7.3:
Frequency-Dependent Material / 7.3.1:
Alternative Meshing Schemes / 7.3.2:
Antenna Array / 7.4:
Electromagnetic Scattering / 7.4.2:
Finite-Element Time Domain Method / Roy ; Salazar-Palma ; Djordjevic7.5:
Incident Field / 8.1:
Transverse Magnetic Case / 8.2:
Formulation / 8.2.1:
Finite-Element Procedure / 8.2.2:
Time-Stepping Procedure / 8.2.3:
Numerical Results / 8.2.4:
Transverse Electric Case / 8.3:
Finite-Volume Time Domain Method / Bonnet ; Ferrieres ; Michielsen ; Klotz ; Roumiguieres8.3.1:
Maxwell's Equations as a Hyperbolic Conservative System / 9.1:
The Conservative Form of Maxwell's Equations / 9.1.1:
Characteristics and Wavefront Propagation / 9.1.2:
An Elementary Form of the Finite-Volume Method / 9.1.3:
Finite-Volume Discretization of Maxwell's Equations / 9.2:
Spatial Discretizations / 9.2.1:
Temporal Discretization / 9.2.2:
Consistency and Stability / 9.2.3:
Hybridization of the FVTD Method with Other Models and Methods / 9.3:
Thin-Wire Models in the FVTD Method / 9.3.1:
Hybridization of the FVTD and the FDTD Methods / 9.3.2:
Another Approach of the Finite-Volume Approach / 9.3.3:
Dielectric Structures / 9.4:
Thin Screens with Finite Conductivity / 9.4.2:
Thin Wires / 9.4.3:
Index / 9.5:
Preface
Acknowledgments
Contributors
8.

図書

図書
Eusebius Doedel, Laurette S. Tuckerman, editors
出版情報: New York : Springer, c2000  x, 471 p. ; 25 cm
シリーズ名: The IMA volumes in mathematics and its applications ; v. 119
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9.

図書

図書
George Emanuel
出版情報: Boca Raton, FL : Chapman & Hall/CRC, 2001  220 p.
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目次情報: 続きを見る
Preface
Background / I:
Introduction / 1:
Continuous One-Parameter Groups-I / 2:
Group Concept / 2.1:
Infinitesimal Transformation / 2.2:
Global Group Equations / 2.3:
Problems / 2.4:
Method of Characteristics / 3:
Theory / 3.1:
Examples / 3.2:
Continuous One-Parameter Groups-II / 3.3:
Invariance / 4.1:
The Once-Extended Group / 4.2:
Higher-Order Extended Groups / 4.3:
Ordinary Differential Equations / 4.4:
First-Order ODEs / 5:
Invariance Under a One-Parameter Group / 5.1:
Canonical Coordinates / 5.2:
Special Procedures / 5.3:
Compendium / 5.4:
Higher-Order ODEs / 5.5:
Invariant Equations / 6.1:
Finding the Groups / 6.2:
System of First-Order ODEs / 6.3:
Second-Order ODEs / 6.4:
Classification of Two-Parameter Groups / 7.1:
Invariance and Canonical Coordinates / 7.2:
Appendices / 7.3:
Bibliography and References / A:
The Rotation Group / B:
Basic Relations / C:
Tables / D:
Answers to Selected Problems / E:
Preface
Background / I:
Introduction / 1:
10.

図書

図書
J.W. Neuberger
出版情報: Berlin : Springer-Verlag, c1997  viii, 149 p. ; 24 cm
シリーズ名: Lecture notes in mathematics ; 1670
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