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Mattheij R.M. — Partial differential equations
Mattheij R.M. — Partial differential equations

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Название: Partial differential equations

Автор: Mattheij R.M.

Аннотация:

Partial differential equations (PDEs) are used to describe a large variety of physical phenomena, from fluid flow to electromagnetic fields, and are indispensable to such disparate fields as aircraft simulation and computer graphics. While most existing texts on PDEs deal with either analytical or numerical aspects of PDEs, this innovative and comprehensive textbook features a unique approach that integrates analysis and numerical solution methods and includes a third component—modeling—to address real-life problems. The authors believe that modeling can be learned only by doing; hence a separate chapter containing 16 user-friendly case studies of elliptic, parabolic, and hyperbolic equations is included and numerous exercises are included in all other chapters. Partial Differential Equations: Modeling, Analysis, Computation enables readers to deepen their understanding of a topic ubiquitous in mathematics and science and to tackle practical problems. The advent of fast computers and the development of numerical methods have enabled the modern engineer to use a large variety of packages to find numerical approximations to solutions of PDEs. Problems are usually standard and a thorough knowledge of a well-chosen subset of analytical and numerical tools and methodologies is necessary when dealing with real-life problems. When one is dealing with PDEs in practice, it becomes clear that both numerical and analytical treatments of the problem are needed. This comprehensive book is intended for graduate students in applied mathematics, engineering, and physics and may be of interest to advanced undergraduate students. Mathematicians, scientists, and engineers also will find the book useful. Contents List of Figures; List of Tables; Notation; Preface; Chapter 1: Differential and difference equations; Chapter 2: Characterization and classification; Chapter 3: Fourier theory; Chapter 4: Distributions and fundamental solutions; Chapter 5: Approximation by finite differences; Chapter 6: The Equations of continuum mechanics and electromagnetics; Chapter 7: The art of modeling; Chapter 8: The analysis of elliptic equations; Chapter 9: Numerical methods for elliptic equations; Chapter 10: Analysis of parabolic equations; Chapter 11: Numerical methods for parabolic equations; Chapter 12: Analysis of hyperbolic equations; Chapter 13: Numerical methods for scalar hyperbolic equations; Chapter 14: Numerical methods for hyperbolic systems; Chapter 15: Perturbation methods; Chapter 16: Modeling, analyzing, and simulating problems from practice; Appendices: Useful definitions and properties; Bibliography; Index.


Язык: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 2005

Количество страниц: 699

Добавлена в каталог: 04.02.2014

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
$\nu$ method      89 273
2-norm      98
Absence of free magnetic poles      123
Acoustic impedance      623
Acoustic liner      623
Adams methods      90
Adams — Bashforth      90
Adams — Moulton      90
ADI (Alternating Direction Implicit)      213 294
Adiabatic invariants      492
Adjoint operator      58
Advection-diffusion barrier      375
Advection-diffusion equation      295 373
Air-damped resonator      488
Aircraft engine noise      622
Alternating direction implicit (ADI)      213 294
Ampere — Maxwell's law      122
Amplification factor      261 365
Amplitude error      371
Approximate Riemann solver      426
Artificial diffusion      378
Associated matrix norm      638
Asymptotic approximation      461
Asymptotic expansion      462
Asymptotic sequence      462
Asymptotically equal      463
Averaging      351
Backward difference      79 90 631
Backward difference formulae (BDF)      86
Backward Euler method      89
Band matrix      208
Barotropic flow      154
Base characteristic      15
BDF (Backward Difference Formulas)      90 632
Beam — Warming scheme      414
Block tridiagonal      208
Block-wave function      37
Blokhintzev invariant      567
Boundary basis vectors      616
Boundary condition      160
Boundary condition, absorbing      448
Boundary condition, nonreflecting      448
Boundary condition, top layer      616
Boundary layer      92 476
Box scheme      189 203 379
Buckley — Leverett equation      326
Catalytic reaction      555
Cauchy problem      334
Cauchy — Schwarz inequality      638
Cauchy's equation of motion      114
Causal      41
Causality condition      41 136
Cell-centered finite volume method      85
Central difference      79 80
CFL (Courant — Friedrichs — Lewy) condition      366
Characteristic equations      15
Characteristic polynomial      639
Characteristic strip equations      316
Characteristic variables      18 330
Characteristics      15 308
Charpit's equations      316
Classical Runge — Kutta      89
Closure      212
Collocation      78
Complementary error function      144 236
Conductive flux      85
Cone of normals      315
Conservation equation      109 311
Conservation law      86
Conservation of angular momentum      113
Conservation of electric charge      123
Conservation of energy      115
Conservation of linear momentum      113
Conservative      46
Conservative scheme      390
Consistency      98
Consistency, explicit Euler scheme      263
Constitutive equations      116
Constitutive relations      109
Contact angle      120
Contact discontinuity      340
Continuum physics      109
Control volume      85
Convective flux      85
Convergence, explicit Euler scheme      264
Convergence, pointwise      631
Convergence, uniform      631
Convolution theorem      39
Correspondence principle      477
Coulomb's law      122
Courant number      364
Courant — Friedrichs — Lewy (CFL) condition      366
Crank — Nicolson scheme      272
Critical rarefaction wave      438
Critical state      439
Cylindrical symmetry      83
D'Alembert solution      350
Dam break problem      435
Damped Newton      218
Damping factor      218
Davidenko equation      222
Decibel      147
Delta function      54
Descent direction      218
Difference equation      76
Difference scheme      80
Diffusion number      261
Dimensionally homogeneous      138
Dimensionless parameter      138 646
Dirichlet boundary condition      160
Discrete dispersion relation      364
Discrete Green's function      214
Discrete pressure gradient      619
Discretisation      77
Discretisation, backward differences      619
Discretisation, forward differences      619
dispersion      45
Displacement vector      110
Distinguished limit      464 477
distribution      54
Distribution, regular      54
Divergence theorem      642
DuFort-Frankel scheme      305
Duhamel integral      63 64
Eckert number      150
Edge condition      136
Eigenvalue      639
Eigenvector      639
Eikonal equation      315
Elasticity      120
Electromagnetic continuity conditions      127
Electrophoresis      599
Energy      484
Energy velocity      45
Enthalpy      118 248
entropy      118
Entropy condition      325
Entropy solution      325
Equispaced      72
Equivalent norms      638
Error function      236
Essential root      91 383
Essential solution      91 383
Euclidean vector space      644
Euler number      150
Expansion shock      323
Explicit Euler method      76 89
Explicit Euler scheme      261
Explicit method      89
Explicit midpoint rule      91
Faraday — Henry's law      122
Fick's law      118
Finite difference      73
Fisher's equation      252
Flux      85
Flux function      310
Flux limiter      397
Flux vector      331
Forward difference      79
Forward Euler Method      89
Fourier cosine series      37
Fourier discrete transform      43
Fourier mode      34
Fourier number      150
Fourier series      34 35
Fourier sine series      37
Fourier transform      38
Fourier's law      117
Fredholm's alternative      62
frequency      34 261
Galloping transmission lines      531
Gauss — Jacobi iteration      209
Gauss — Seidel iteration      209
Gauss's theorem      642
Generalised eigenvalue problem      327
Generalized Riemann problem      404
Genuinely nonlinear      337
Geometric multiplicity      640
Geopotential      342
Glass oven      613
Glass production      581
Global discretisation error      193 263
Global discretisation error, implicit Euler method      271
Global discretisation error, vector      99
Godunov scheme      388 423
Godunov scheme, wave propagation form      425
Green's first identity      642
Green's function      61 174
Groundwater flow      540
Group velocity      45 565
Growth factor      103
Harmonic function      160
Harten — Hyman entropy fix      439
heat capacity      119
Heat equation      24 233 260
Heat flow in a bar      469
Helmholtz equation      8 159
Helmholtz number      150
High-resolution flux      398
High-resolution scheme      391 398
Homogeneous      214
Hooke's law      120
Hyperbolic equation      308
Hyperbolic equation, conservation form      310
Hyperbolic equation, linear      308
Hyperbolic equation, quasi-linear      310
Hyperbolic equation, semilinear      309
Hyperbolic system      329
Hyperbolic system, characteristic form      331
Hyperbolic system, conservation form      331
Hyperbolic system, linear      328
Hyperbolic system, normal form      331
Hyperbolic system, quasi-linear      330
Implicit Euler method      76 89
Implicit Euler scheme      270
Implicit method      89 90
Incremental form      392
Infinity norm      98
Inherent scaling      138
Initial curve      15
Initial value      96
Inner expansion      476
Integral surface      13
Interior layers      92
Internal layer      476
Interpolation points      72
Isotachophoresis      599
Iteration matrix      208
Iterative methods      208
Jordan normal form      640
Joukowski transformation      153
Joule heating      124
k-rarefaction wave      339
k-Riemann invariants      339
k-shock wave      341
k-simple wave      339
Kelvin — Voigt model      121
Kelvin's theorem      126
Kutta condition      154
Lagrangian basis polynomials      72
Lagrangian interpolation polynomial      72
Laplace equation      24 159
Laser drilling      589
Latent heat      119
Lax — Friedrichs scheme      414
Lax — Wendroff scheme      368
Layers      92
Leapfrog scheme      382
Left eigenvectors      327
Limiter, function      397
Limiter, superbee      402
Limiter, van Leer      402
Lindstedt — Poincare method      473
Linearly degenerate      338
Local discretisation error      78 189 193 263 366
Local discretisation error, $\nu$ method      274
Local discretisation error, Lax — Wendroff scheme      369
Local discretisation error, upwind scheme      366
Local discretisation error, vector      98
Logarithmic switchback      481
Longitudinal      96
Longitudinal method of lines      265
Lorentz force      125
Lubrication flow      496
Mach number      150
Matched asymptotic expansions (MAEs)      475 477
Matching      477 483
Material surface      111
Material volume      111
Mathematising      130
Matrix method      276
Matrix pencil      328
Matrix pencil, regular      328
Matrix pencil, singular      328
Matrix, defect      641
Matrix, similarity transformation      640
Matrix, stable      641
Matrix, trace      639
Maxwell equations      123
Maxwell model      122
Median 2-norm      98
Method of lines (MOL)      96
Method of Massau      333
Method of strained coordinates      474 486
Midpoint formula      75
Midpoint rule      89
Minmod slope      407
Mixed boundary conditions      282
MODE      147
Model      131
Model, asymptotic      131
Model, building block      132
Model, canonical      135
Model, characteristic      135
Model, constructing      132
Model, lumped parameter      132
Model, quintessential      131
Model, systematic      131
Modified equation      421
MOL (method of lines)      96
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