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1.

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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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:
2.

図書

図書
Arieh Iserles
出版情報: Cambridge : Cambridge University Press, 2009  xviii, 459 p. ; 25 cm
シリーズ名: Cambridge texts in applied mathematics
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Preface to the second edition
Preface to the first edition
Flowchart of contents
Ordinary differential equations / I:
Euler's method and beyond / 1:
Ordinary differential equations and the Lipschitz condition / 1.1:
Euler's method / 1.2:
The trapezoidal rule / 1.3:
The theta method / 1.4:
Comments and bibliography
Exercises
Multistep methods / 2:
The Adams method / 2.1:
Order and convergence of multistep methods / 2.2:
Backward differentiation formulae / 2.3:
Runge-Kutta methods / 3:
Gaussian quadrature / 3.1:
Explicit Runge-Kutta schemes / 3.2:
Implicit Runge-Kutta schemes / 3.3:
Collocation and IRK methods / 3.4:
Stiff equations / 4:
What are stiff ODEs? / 4.1:
The linear stability domain and A-stability / 4.2:
A-stability of Runge-Kutta methods / 4.3:
A-stability of multistep methods / 4.4:
Geometric numerical integration / 5:
Between quality and quantity / 5.1:
Monotone equations and algebraic stability / 5.2:
From quadratic invariants to orthogonal flows / 5.3:
Hamiltonian systems / 5.4:
Error control / 6:
Numerical software vs. numerical mathematics / 6.1:
The Milne device / 6.2:
Embedded Runge-Kutta methods / 6.3:
Nonlinear algebraic systems / 7:
Functional iteration / 7.1:
The Newton-Raphson algorithm and its modification / 7.2:
Starting and stopping the iteration / 7.3:
The Poisson equation / II:
Finite difference schemes / 8:
Finite differences / 8.1:
The finite element method / 8.2:
Two-point boundary value problems / 9.1:
A synopsis of FEM theory / 9.2:
Spectral methods / 9.3:
Sparse matrices vs. small matrices / 10.1:
The algebra of Fourier expansions / 10.2:
The fast Fourier transform / 10.3:
Second-order elliptic PDEs / 10.4:
Chebyshev methods / 10.5:
Gaussian elimination for sparse linear equations / 11:
Banded systems / 11.1:
Graphs of matrices and perfect Cholesky factorization / 11.2:
Classical iterative methods for sparse linear equations / 12:
Linear one-step stationary schemes / 12.1:
Classical iterative methods / 12.2:
Convergence of successive over-relaxation / 12.3:
Multigrid techniques / 12.4:
In lieu of a justification / 13.1:
The basic multigrid technique / 13.2:
The full multigrid technique / 13.3:
Poisson by multigrid / 13.4:
Conjugate gradients / 14:
Steepest, but slow, descent / 14.1:
The method of conjugate gradients / 14.2:
Krylov subspaces and preconditioners / 14.3:
Poisson by conjugate gradients / 14.4:
Fast Poisson solvers / 15:
TST matrices and the Hockney method / 15.1:
Fast Poisson solver in a disc / 15.2:
Partial differential equations of evolution / III:
The diffusion equation / 16:
A simple numerical method / 16.1:
Order, stability and convergence / 16.2:
Numerical schemes for the diffusion equation / 16.3:
Stability analysis I: Eigenvalue techniques / 16.4:
Stability analysis II: Fourier techniques / 16.5:
Splitting / 16.6:
Hyperbolic equations / 17:
Why the advection equation? / 17.1:
Finite differences for the advection equation / 17.2:
The energy method / 17.3:
The wave equation / 17.4:
The Burgers equation / 17.5:
Appendix Bluffer's guide to useful mathematics
Linear algebra / A.1:
Vector spaces / A.1.1:
Matrices / A.1.2:
Inner products and norms / A.1.3:
Linear systems / A.1.4:
Eigenvalues and eigenvectors / A.1.5:
Bibliography
Analysis / A.2:
Introduction to functional analysis / A.2.1:
Approximation theory / A.2.2:
Index / A.2.3:
Preface to the second edition
Preface to the first edition
Flowchart of contents
3.

図書

図書
J.C. Butcher
出版情報: Chichester : Wiley, c2003  xiv, 425 p. ; 24 cm
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Preface
Differential and Difference Equations / 1:
Differential Equation Problems / 10:
Differential Equation Theory / 11:
Difference Equation Problems / 100:
Introduction to differential equations
Difference Equation Theory / 13:
The Kepler problem / 2:
Numerical Differential Equation Methods
The Euler Method / 102:
Many-body gravitational problems
Analysis of the Euler Method / 21:
A problem arising from the method of lines / 22:
Generalizations of the Euler Method
Runge-Kutta Methods / 104:
The simple pendulum
Linear Multistep Methods / 24:
A chemical kinetics problem / 25:
Taylor Series Methods
Hybrid Methods / 106:
The van der Pol equation and limit cycles
The Lotka-Volterra problem and periodic orbits / 3:
Preliminaries
Order Conditions / 31:
Low Order Explicit Methods / 32:
Existence and uniqueness of solutions / 33:
Runge-Kutta Methods with Error Estimates
Implicit Runge-Kutta Methods / 111:
Linear systems of differential equations
Stability of Implicit Runge-Kutta Methods / 35:
Stiff differential equations / 36:
Implementable Implicit Runge-Kutta Methods
Order Barriers / 113:
Laplace transforms
Algebraic Properties of Runge-Kutta Methods / 38:
Implementation Issues / 39:
Introduction to difference equations / 120:
A linear problem / 40:
The Order of Linear Multistep Methods
Errors and Error Growth / 122:
The Fibonacci difference equation
Stability Characteristics / 43:
Three quadratic problems / 44:
Order and Stability Barriers
One-leg Methods and G-stability / 124:
Iterative solutions of a polynomial equation
The arithmetic-geometric mean / 46:
General Linear Methods
Representing Methods in General Linear Form / 50:
Consistency, Stability and Convergence / 51:
Linear difference equations / 52:
The Stability of General Linear Methods
The Order of General Linear Methods / 131:
Constant coefficients
Methods with Runge-Kutta Stabiulity / 54:
References
Powers of matrices
Index
The Z-transform / 133:
Introduction to the Euler method / 200:
Some numerical experiments / 201:
Calculations with stepsize control / 202:
Calculations with mildly stiff problems / 203:
Calculations with the implicit Euler method / 204:
Formulation of the Euler method / 210:
Local truncation error / 211:
Global truncation error / 212:
Convergence of the Euler method / 213:
Order of convergence / 214:
Asymptotic error formula / 215:
Stability characteristics / 216:
Local truncation error estimation / 217:
Rounding error / 218:
Introduction / 220:
More computations in a step / 221:
Greater dependence on previous values / 222:
Use of higher derivatives / 223:
Multistep-multistage-multiderivative methods / 224:
Implicit methods / 225:
Local error estimates / 226:
Historical introduction / 230:
Second order methods / 231:
The coefficient tableau / 232:
Third order methods / 233:
Introduction to order conditions / 234:
Fourth order methods / 235:
Higher orders / 236:
Implicit Runge-Kutta methods / 237:
Numerical examples / 238:
Adams methods / 240:
General form of linear multistep methods / 242:
Consistency, stability and convergence / 243:
Predictor-corrector Adams methods / 244:
The Milne device / 245:
Starting methods / 246:
Introduction to Taylor series methods / 247:
Manipulation of power series / 251:
An example of a Taylor series solution / 252:
Other methods using higher derivatives / 253:
The use of f derivatives / 254:
Further numerical examples / 255:
Pseudo Runge-Kutta methods / 260:
Generalized linear multistep methods / 262:
General linear methods / 263:
Rooted trees / 264:
Functions on trees / 301:
Some combinatorial questions / 302:
The use of labelled trees / 303:
Differentiation / 304:
Taylor's theorem / 305:
Elementary differentials / 310:
The Taylor expansion of the exact solution / 311:
Elementary weights / 312:
The Taylor expansion of the approximate solution / 313:
Independence of the elementary differentials / 314:
Conditions for order / 315:
Order conditions for scalar problems / 316:
Independence of elementary weights / 317:
Methods of orders less than four / 318:
Simplifying assumptions / 321:
Methods of order four / 322:
New methods from old / 323:
Methods of order five / 324:
Methods of order six / 325:
Methods of orders greater than six / 326:
Richardson error estimates / 330:
Methods with built-in estimates / 332:
A class of error-estimating methods / 333:
The methods of Fehlberg / 334:
The methods of Verner / 335:
The methods of Dormand and Prince / 336:
Solvability of implicit equations / 340:
Methods based on Gaussian quadrature / 342:
Reflected methods / 343:
Methods based on Radau and Lobatto quadrature / 344:
A-stability, A([alpha])-stability and L-stability / 350:
Criteria for A-stability / 351:
Pade approximations to the exponential function / 352:
A-stability of Gauss and related methods / 353:
Order stars / 354:
Order arrows and the Ehle barrier / 355:
AN-stability / 356:
Non-linear stability / 357:
BN-stability of collocation methods / 358:
The V and W transformations / 359:
Implementation of implicit Runge-Kutta methods / 360:
Diagonally-implicit Runge-Kutta methods / 361:
The importance of high stage order / 362:
Singly implicit methods / 363:
Generalizations of singly-implicit methods / 364:
Effective order and DESIRE methods / 365:
Explicit barriers / 370:
An upper bound on the required number of stages / 371:
Motivation / 380:
Equivalence classes of Runge-Kutta methods / 381:
The group of Runge-Kutta methods / 382:
The Runge-Kutta group / 383:
A homomorphism between two groups / 384:
A generalization of G[subscript 1] / 385:
Recursive formula for the product / 386:
Some special elements of G / 387:
Some subgroups and quotient groups / 388:
An algebraic interpretation of effective order / 389:
Optimal sequences / 390:
Acceptance and rejection of steps / 392:
Error per step versus error per unit step / 393:
Control theoretic considerations / 394:
Solving the implicit equations / 395:
Fundamentals / 400:
Convergence / 401:
Stability / 403:
Consistency / 404:
Necessity of conditions for convergence / 405:
Sufficiency of conditions for convergence / 406:
Criteria for order / 410:
Derivation of methods / 411:
Backward difference methods / 412:
Further remarks on error growth / 420:
The underlying one-step method / 422:
Weakly stable methods / 423:
Variable stepsize / 424:
Stability regions / 430:
Examples of the boundary locus method / 432:
Examples of the Schur criterion / 433:
Stability of predictor-corrector methods / 434:
Survey of barrier results / 440:
Maximum order for a convergent k step method / 441:
Order stars for linear multistep methods / 442:
Order arrows for linear multistep methods / 443:
The one-leg counterpart to a linear multistep method / 450:
The concept of G-stability / 451:
Transformations relating one-leg and linear multistep methods / 452:
Effective order interpretation / 453:
Concluding remarks on G-stability / 454:
Survey of implementation considerations / 460:
Representation of data / 461:
Variable stepsize for Nordsieck methods / 462:
Local error estimation / 463:
Multivalue multistage methods / 500:
Transformations of methods / 501:
Runge-Kutta methods as general linear methods / 502:
Linear multistep methods as general linear methods / 503:
Some known unconventional methods / 504:
Some recently discovered general linear methods / 505:
Definitions of consistency and stability / 510:
Covariance of methods / 511:
Definition of convergence / 512:
The necessity of stability / 513:
The necessity of consistency / 514:
Stability and consistency imply convergence / 515:
Methods with maximal stability order / 520:
Possible definitions of order / 530:
Algebraic analysis of order / 531:
An example of the algebraic approach to order / 532:
Methods with Runge-Kutta stability / 533:
Design criteria for general linear methods / 540:
The types of DIMSIM methods / 541:
Runge-Kutta stability / 542:
Almost Runge-Kutta methods / 543:
Fourth order, four stage ARK methods / 544:
Doubly companion matrices / 545:
Inherent Runge-Kutta stability / 546:
Derivation of methods with IRK stability / 547:
Some nonstiff methods / 548:
Some stiff methods / 549:
Preface
Differential and Difference Equations / 1:
Differential Equation Problems / 10:
4.

図書

図書
Hans J. Stetter
出版情報: Berlin ; New York : Springer, 1973  xvi, 388 p. ; 24 cm
シリーズ名: Springer tracts in natural philosophy ; v. 23
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5.

図書

図書
Carl M. Bender, Steven A. Orszag
出版情報: New York ; Tokyo : McGraw-Hill, c1978  xiv, 593 p. ; 25 cm
シリーズ名: International series in pure and applied mathematics
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6.

図書

図書
J. Kevorkian, J.D. Cole
出版情報: New York : Springer-Verlag, c1981  x, 558 p. ; 25 cm
シリーズ名: Applied mathematical sciences ; v. 34
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7.

図書

図書
Ali Hasan Nayfeh
出版情報: New York : Wiley, c1973  xii, 425 p. ; 23 cm
シリーズ名: Pure and applied mathematics
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Introduction / 1.:
Parameter Perturbations / 1.1.:
An Algebraic Equation / 1.1.1.:
The van der Pol Oscillator / 1.1.2.:
Coordinate Perturbations / 1.2.:
The Bessel Equation of Zeroth Order / 1.2.1.:
A Simple Example / 1.2.2.:
Order Symbols and Gauge Functions / 1.3.:
Asymptotic Expansions and Sequences / 1.4.:
Asymptotic Series / 1.4.1.:
Asymptotic Expansions / 1.4.2.:
Uniqueness of Asymptotic Expansions / 1.4.3.:
Convergent versus Asymptotic Series / 1.5.:
Nonuniform Expansions / 1.6.:
Elementary Operations on Asymptotic Expansions / 1.7.:
Exercises
Straightforward Expansions and Sources of Nonuniformity / 2.:
Infinite Domains / 2.1.:
The Duffing Equation / 2.1.1.:
A Model for Weak Nonlinear Instability / 2.1.2.:
Supersonic Flow Past a Thin Airfoil / 2.1.3.:
Small Reynolds Number Flow Past a Sphere / 2.1.4.:
A Small Parameter Multiplying the Highest Derivative / 2.2.:
A Second-Order Example / 2.2.1.:
High Reynolds Number Flow Past a Body / 2.2.2.:
Relaxation Oscillations / 2.2.3.:
Unsymmetrical Bending of Prestressed Annular Plates / 2.2.4.:
Type Change of a Partial Differential Equation / 2.3.:
Long Waves on Liquids Flowing down Incline Planes / 2.3.1.:
The Presence of Singularities / 2.4.:
Shift in Singularity / 2.4.1.:
The Earth-Moon-Spaceship Problem / 2.4.2.:
Thermoelastic Surface Waves / 2.4.3.:
Turning Point Problems / 2.4.4.:
The Role of Coordinate Systems / 2.5.:
The Method of Strained Coordinates / 3.:
The Method of Strained Parameters / 3.1.:
The Lindstedt-Poincare Method / 3.1.1.:
Transition Curves for the Mathieu Equation / 3.1.2.:
Characteristic Exponents for the Mathieu Equation (Whittaker's Method) / 3.1.3.:
The Stability of the Triangular Points in the Elliptic Restricted Problem of Three Bodies / 3.1.4.:
Characteristic Exponents for the Triangular Points in the Elliptic Restricted Problem of Three Bodies / 3.1.5.:
A Simple Linear Eigenvalue Problem / 3.1.6.:
A Quasi-Linear Eigenvalue Problem / 3.1.7.:
The Quasi-Linear Klein-Gordon Equation / 3.1.8.:
Lighthill's Technique / 3.2.:
A First-Order Differential Equation / 3.2.1.:
The One-Dimensional Earth-Moon-Spaceship Problem / 3.2.2.:
A Solid Cylinder Expanding Uniformly in Still Air / 3.2.3.:
Expansions by Using Exact Characteristics--Nonlinear Elastic Waves / 3.2.4.:
Temple's Technique / 3.3.:
Renormalization Technique / 3.4.:
Limitations of the Method of Strained Coordinates / 3.4.1.:
The Methods of Matched and Composite Asymptotic Expansions / 3.5.1.:
The Method of Matched Asymptotic Expansions / 4.1.:
Introduction--Prandtl's Technique / 4.1.1.:
Higher Approximations and Refined Matching Procedures / 4.1.2.:
A Second-Order Equation with Variable Coefficients / 4.1.3.:
Reynolds' Equation for a Slider Bearing / 4.1.4.:
The Method of Composite Expansions / 4.1.5.:
A Second-Order Equation with Constant Coefficients / 4.2.1.:
An Initial Value Problem for the Heat Equation / 4.2.2.:
Limitations of the Method of Composite Expansions / 4.2.4.:
Variation of Parameters and Methods of Averaging / 5.:
Variation of Parameters / 5.1.:
Time-Dependent Solutions of the Schrodinger Equation / 5.1.1.:
A Nonlinear Stability Example / 5.1.2.:
The Method of Averaging / 5.2.:
Van der Pol's Technique / 5.2.1.:
The Krylov-Bogoliubov Technique / 5.2.2.:
The Generalized Method of Averaging / 5.2.3.:
Struble's Technique / 5.3.:
The Krylov-Bogoliubov-Mitropolski Technique / 5.4.:
The Duffiing Equation / 5.4.1.:
The Klein-Gordon Equation / 5.4.2.:
The Method of Averaging by Using Canonical Variables / 5.5.:
The Mathieu Equation / 5.5.1.:
A Swinging Spring / 5.5.3.:
Von Zeipel's Procedure / 5.6.:
Averaging by Using the Lie Series and Transforms / 5.6.1.:
The Lie Series and Transforms / 5.7.1.:
Generalized Algorithms / 5.7.2.:
Simplified General Algorithms / 5.7.3.:
A Procedure Outline / 5.7.4.:
Algorithms for Canonical Systems / 5.7.5.:
Averaging by Using Lagrangians / 5.8.:
A Model for Dispersive Waves / 5.8.1.:
A Model for Wave-Wave Interaction / 5.8.2.:
The Nonlinear Klein-Gordon Equation / 5.8.3.:
The Method of Multiple Scales / 6.:
Description of the Method / 6.1.:
Many-Variable Version (The Derivative-Expansion Procedure) / 6.1.1.:
The Two-Variable Expansion Procedure / 6.1.2.:
Generalized Method--Nonlinear Scales / 6.1.3.:
Applications of the Derivative-Expansion Method / 6.2.:
Forced Oscillations of the van der Pol Equation / 6.2.1.:
Parametric Resonances--The Mathieu Equation / 6.2.4.:
The van der Pol Oscillator with Delayed Amplitude Limiting / 6.2.5.:
Limitations of the Derivative-Expansion Method / 6.2.6.:
Limitations of This Technique / 6.3.:
Generalized Method / 6.4.:
A General Second-Order Equation with Variable Coefficients / 6.4.1.:
A Linear Oscillator with a Slowly Varying Restoring Force / 6.4.3.:
An Example with a Turning Point / 6.4.4.:
The Duffing Equation with Slowly Varying Coefficients / 6.4.5.:
Reentry Dynamics / 6.4.6.:
Advantages and Limitations of the Generalized Method / 6.4.7.:
Asymptotic Solutions of Linear Equations / 7.:
Second-Order Differential Equations / 7.1.:
Expansions Near an Irregular Singularity / 7.1.1.:
An Expansion of the Zeroth-Order Bessel Function for Large Argument / 7.1.2.:
Liouville's Problem / 7.1.3.:
Higher Approximations for Equations Containing a Large Parameter / 7.1.4.:
Homogeneous Problems with Slowly Varying Coefficients / 7.1.5.:
Reentry Missile Dynamics / 7.1.7.:
Inhomogeneous Problems with Slowly Varying Coefficients / 7.1.8.:
Successive Liouville-Green (WKB) Approximations / 7.1.9.:
Systems of First-Order Ordinary Equations / 7.2.:
Expansions Near an Irregular Singular Point / 7.2.1.:
Asymptotic Partitioning of Systems of Equations / 7.2.2.:
Subnormal Solutions / 7.2.3.:
Systems Containing a Parameter / 7.2.4.:
Homogeneous Systems with Slowly Varying Coefficients / 7.2.5.:
The Langer Transformation / 7.3.:
Problems with Two Turning Points / 7.3.3.:
Higher-Order Turning Point Problems / 7.3.4.:
Higher Approximations / 7.3.5.:
An Inhomogeneous Problem with a Simple Turning Point--First Approximation / 7.3.6.:
An Inhomogeneous Problem with a Simple Turning Point--Higher Approximations / 7.3.7.:
An Inhomogeneous Problem with a Second-Order Turning Point / 7.3.8.:
Turning Point Problems about Singularities / 7.3.9.:
Turning Point Problems of Higher Order / 7.3.10.:
Wave Equations / 7.4.:
The Born or Neumann Expansion and The Feynman Diagrams / 7.4.1.:
Renormalization Techniques / 7.4.2.:
Rytov's Method / 7.4.3.:
A Geometrical Optics Approximation / 7.4.4.:
A Uniform Expansion at a Caustic / 7.4.5.:
The Method of Smoothing / 7.4.6.:
References and Author Index
Subject Index
Introduction / 1.:
Parameter Perturbations / 1.1.:
An Algebraic Equation / 1.1.1.:
8.

図書

図書
J. R. Cash
出版情報: London ; New York : Academic Press, 1979  xii, 223 p. ; 24 cm
シリーズ名: Computational mathematics and applications
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9.

図書

図書
L. Fox and D.F. Mayers
出版情報: London ; New York : Chapman and Hall, 1987  xi, 249 p. ; 24 cm
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10.

図書

図書
E. Hairer, S.P. Nørsett, G. Wanner
出版情報: Berlin ; Tokyo : Springer-Verlag, c1987  xiii, 480 p. ; 24 cm
シリーズ名: Springer series in computational mathematics ; 8 . Solving ordinary differential equations ; 1
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