Главная    Ex Libris    Книги    Журналы    Статьи    Серии    Каталог    Wanted    Загрузка    ХудЛит    Справка    Поиск по индексам    Поиск    Форум   
blank
Авторизация

       
blank
Поиск по указателям

blank
blank
blank
Красота
blank
Mattheij R.M.M. — Partial differential equations: modeling, analysis, computation
Mattheij R.M.M. — Partial differential equations: modeling, analysis, computation



Обсудите книгу на научном форуме



Нашли опечатку?
Выделите ее мышкой и нажмите Ctrl+Enter


Название: Partial differential equations: modeling, analysis, computation

Автор: Mattheij R.M.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: 665

Добавлена в каталог: 19.10.2010

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
blank
Предметный указатель
MOL (method of lines)      96
Monge cone      315
Monocrystalline silicon bar      547
Multiple scales      483 484 486
Multiplicity, algebraic      641
Multiplicity, geometric      641
Multistep      77
Multistep method      90
Navier - Stokes equations      119
Neumann boundary condition      160
Newton update      217
Newton's method      217
Nondissipative scheme      379
Nonlinear first order equation, characteristic form      314
Numerical boundary condition      409 449
Numerical diffusion      377
Numerical domain of dependence      366
Numerical flux      387 391
Numerical group velocity      384
Numerical phase velocity      371
Objective      117
Observer transformation      117
Ohm's law      124
Operator splitting      213
Orthogonally invariant      639
Outer expansion      476
Overlap hypothesis      476
P$\acute{e}$clet number      150 376
Page      662 0
Parasitic root      91
Parasitic solutions      91
Parison      582
Parseval's identity      35
Particular      61
Particular solution      173
Pendulum      474
Perfect gas      119
Permafrost      157
Perturbation methods      464
Pfaffian differential equation      330
Phase angle      261 365
phase velocity      45 370
Physical boundary conditions      354
Physical model      116
Piecewise continuous      34
Piecewise smooth      34
Poincar$\acute{e}$ expansion      466
Poiseuille flow      151
Poisson equation      159
Poisson's formula      40
Poisson's ratio      121
Powder blasting      508
Powder erosion      508
Poynting's theorem      124
Prandtl number      150
Prandtl's boundary layer      480 481
Preface      xxxi
Pressure correction algorithm      224
Pressure correction method      223
Pressure Poisson equation      222
Pressure, mechanical      120
Pressure, thermodynamic      120
Principal curvatures      120
Pulse tube refrigerator      606
Quadrature formula      75
Quasi one-dimensional gas dynamics      471
Quasi-linear      17
Radiation condition      447
Radiative      244
Rankine - Hugoniot jump condition      320 336
Rarefaction wave      323
Ray acoustics      493 563
Ray approximation      487 493 564
Ray tube      567
Reality condition      41
Reduced equation      93
Reduced wave equation      8
Refinement path      98
Reflections      350
Refraction, temperature gradient      563
Refraction, wind shear      563
Regular expansion      467
Relative phase error      371
Resin curing      501
Resonance      485 486
Reynolds lubrication equations      584
Reynolds number      150
Riemann invariants      331
Riemann problem      322
Riemann variables      331
Robin boundary condition      160
Roe matrix      427
Roe numerical flux      426
Roe scheme      426
Runge - Kutta method      89
Sawtooth function      36
Secular terms      474 475 485 487 489
Self-adjoint      165
Shallow-water equations      342 471 473
Shock speed      322
Shock wave      322
Signal velocity      45
Significant degeneration      464 477
Similarity solutions      25 143
Singular expansion      467
Skew symmetric      640
Slope limiter      405
Slope limiter scheme      405
Slowly varying duct      490
Slowly varying fast time scale      487
Sound attenuation      622
Sparse matrix      206
Specific energy      115
Specific heat      119
Specific heat ratio      119
Specific internal energy      115
Specific kinetic energy      115
Spectral radius      640
Spherical symmetry      83
Spurious mode      224
Spurious root      383
Stability condition, $\vartheta$ method      273
Stability condition, explicit Euler method      263
Stability condition, Lax - Wendroff scheme      369
Stability condition, upwind scheme      367
Stable      99
Stages      78
Staggered grid      225
Stationary elliptic equation      249
Stefan constant      246
Stefan Problem      592
Stencil      80
Stiff      95
Stiffness      95
Stokes equations      152 178 222
Stokes flow      152
Stokes's hypothesis      120
Stokes's theorem      642
Stokeslets      179
Stretch      93
Stretched coordinate      476
Strouhal number      150
Subcritical flow      359
Supercritical flow      358
Superposition      62 174
Superposition principle      215
Support      53
Surface tension      120 498
Suspended bar      497
symmetric      640
Telegraph equation      5
Tensor      644
Tensor, contraction      644
Tensor, deformation velocity      110
Tensor, determinant      644
Tensor, deviator      644
Tensor, divergence      645
Tensor, double inner product      645
Tensor, dyadic product      645
Tensor, inner product      645
Tensor, invariants      644
Tensor, linear deformation      110
Tensor, linear strain      110
Tensor, rate of deformation      110
Tensor, trace      644
Test function      318
Thin-layer flow      570
Time closure      212
Total variation (TV)      392
Total variation diminishing (TVD)      392
Traffic flow equation      324
Transient method      221
Transport equation      311
Transport theorem      111 643
Transversal      96
Trapezoidal formula      75
Trapezoidal rule      89
Travelling wave      25
Travelling-wave solution      253
Triangle inequality      637
TV (total variation)      392
TVD region      399
uniform      77
Uniform asymptotic approximation      461
Upwind scheme      364 419
van der Pol equation      498
Vanishing viscosity solution      314
Variable step, variable order methods      91
Vertex-centered finite volume method      86
Virtual grid points      189 283
Viscoelasticity      121 523
Viscosity, bulk      120
Viscosity, dynamic      120
Viscosity, expansion      120
Viscosity, kinematic      120
Viscosity, second      120
Viscous stress tensor      118
Wave action      493 494
Wave energy      493
Wave equation      24 349
wave number      34 261
Wave speed      25 45
Wave strength      428
Weakly diagonally dominant      202
Webster's horn equation      496
Weights      73 75
WKB (Wentzel - Kramers - Brillouin) hypothesis      487
Young's modulus      121
1 2
blank
Реклама
blank
blank
HR
@Mail.ru
       © Электронная библиотека попечительского совета мехмата МГУ, 2004-2024
Электронная библиотека мехмата МГУ | Valid HTML 4.01! | Valid CSS! О проекте