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Garbey M., Kaper H.G. — Asymptotic Analysis and the Numerical Solution of Partial Differential Equations, Vol. 130
Garbey M., Kaper H.G. — Asymptotic Analysis and the Numerical Solution of Partial Differential Equations, Vol. 130

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Название: Asymptotic Analysis and the Numerical Solution of Partial Differential Equations, Vol. 130

Авторы: Garbey M., Kaper H.G.

Аннотация:

Integrates two fields generally held to be incompatible, if not downright antithetical, in 16 lectures from a February 1990 workshop at the Argonne National Laboratory, Illinois. The topics, of interest to industrial and applied mathematicians, analysts, and computer scientists, include singular per


Язык: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 2001

Количество страниц: 286

Добавлена в каталог: 10.04.2008

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
Accelerating wave      162
Acoustic stability      178
Activation energy      254 256
Aerodynamics, transonic      145
Algebraic manipulation software      241
Analysis, synergism with computation      50
Arrhenius kinetics      162
Asymptotic analysis, domain decomposition methods with      39
Asymptotic analysis, multiple scales problems      77
Asymptotic analysis, singular-perturbation problems      33
Asymptotic approximation      11
Asymptotic boundary conditions      106 109
Asymptotic evaluation of integrals      11
Asymptotic expansion      39 57 58
Asymptotic theory, verification      178
Asymptotically induced domain decomposition      59—77
Asymptotics, diffusion equations      246
Asymptotics, far fields      99 104
Asymptotics, matched      53
Atmospheric approximation      141
Axisymmetric bodies      155
Basin of attraction, boundaries of      26
Bifurcation analysis, with MAPLE      254 258 262
Bifurcation diagrams      261
Bifurcation parameter      257
Bifurcations, vertical      261
Blow-up of solutions of nonlinear heat and wave equations      217
Blow-up points      218
Blow-up time      220
Blow-up, survey article on      219
Boundary conditions, asymptotic      106 109
Boundary conditions, radiation      99
Boundary functions, continuous conditions for      59
Boundary layer problems, elliptic      55
Boundary layer problems, parabolic      56
Boundary layers and multiple scale problems      75
Boundary layers, birth of      39
Boundary layers, interior layer interactions with      14
Boundary layers, ordinary      38
Boundary layers, parabolic      39
Boundary value problems, applications      6 11
Boundary value problems, free      253
Boundary value problems, initial      109 140
Boundary value problems, limiting solutions      5 7 9—11 13
Boundary value problems, positive solutions of      246
Boundary value problems, radial solutions of      246
Boundary value problems, spectral decomposition of solution      37
Boundary value problems, two-point      3 11
Boundary, burnt      111
Bubnov — Galerkin approximation      115 116
Burgers' equation      11 79 176 226 227
Capture of oscillations      26 29
Cauchy problem      219 221 222
Cellular automata      196
Cellular detonation      175 180
Cellular fluids      196
Changing variables, with MAPLE      249
Chaos, molecular      198
Chapman — Enskog analysis      196 202
Chapman — Jouguet velocity      173
Chin — Krasny method      44 45
Choked transonic flow      155
Combustion, bifurcation phenomena, with MAPLE      254
Combustion, condensed phase      254
Combustion, mathematical model      255
Combustion, modeling      108
Combustion, multiple point      255 259
Combustion, nonlinear hyperbolic equation in      222
Combustion, propagation of front      255
Combustion, pulsating waves      259
Combustion, spin      255
Combustion, spinning waves      259
Combustion, standing waves      259
Combustion, theory      223
Combustion, traveling waves      259
Combustion, uniformly propagating plane front      256
Comparison techniques, with MAPLE      250
Connection formulas      17 18 30—31
Conservation laws, classical solution      225
Conservation laws, convergence to steady state      225
Conservation laws, eigensolutions      226 236
Conservation laws, lattice methods      201
Conservation laws, scalar      81
Conservation laws, steady-state solutions      225
Conservation laws, weak solutions      225
Convection-diffusion equation, singularly perturbed      35
Convection-reaction-diffusion equation      45
Coriolis force      137 142
Cylindrical domains      100
Decomposition, global      42
Decomposition, spectral      37
Deflagration      161
Detonation shock dynamics (DSD)      178
Detonation, accelerating subsonic reaction wave with      162
Detonation, applications      178
Detonation, cellular      173
Detonation, cellular wave structure      178
Detonation, CJ velocity      173
Detonation, conventional      162
Detonation, high-speed      159
Detonation, mathematical model      171
Detonation, multidimensional      172
Detonation, near-CJ      173
Detonation, one dimensional      171
Detonation, precursor shock      162
Detonation, reaction zone      171
Detonation, shock and reaction zone      169
Detonation, shock waves      171
Detonation, verification of asymptotic theory      178
Detonation, weak      162
Detonation, weakly curved shock      174
Detonation, ZND model      171
Differential geometry      40
Diffusion equation, semilinear, asymptotics of solutions      246
Diffusion equation, semilinear, boundary value problems      246
Diffusion equation, semilinear, critical exponent      246 249
Diffusion equation, semilinear, Dirichlet problem      247
Diffusion equation, semilinear, existence of solutions      246
Diffusion equation, semilinear, free boundary problem      253
Diffusion equation, semilinear, ground state solution      248
Diffusion equation, semilinear, open problems      249
Diffusion equation, semilinear, positive solutions      246
Diffusion equation, semilinear, radial solutions      246 249
Diffusion equation, semilinear, Sobolev exponent      247 249
Diffusion equation, semilinear, subcritical exponent      247
Diffusion equation, semilinear, supercritical exponent      247
Diffusion equation, semilinear, uniqueness of solutions      246 250 251—253
Dirichlet problem, domain decomposition methods with      32
Dirichlet problem, semilinear diffusion equations with      247
dispersion relation      257
Dissipative perturbations and amplitude of oscillations      17
Dissipative perturbations, illustration      20
Disturbance theory      130
Domain decomposition for convection-diffusion problems      35
Domain decomposition for multiple scales problems      34
Domain decomposition for parabolic boundary layer problems      60
Domain decomposition in parallel computation      32
Domain decomposition method      249
Domain decomposition, asymptotic structure of solution used with      39
Domain decomposition, asymptotically induced      55
Domain decomposition, boundary-fitting charts needed with      52
Domain decomposition, convergence      66
Domain decomposition, divergence      68
Domain decomposition, heterogeneous      137
Domain decomposition, history      33
Domain decomposition, hybrid-perturbation Galerkin method with      130
Domain decomposition, orthogonal polynomials generated with      47
Domain decomposition, spectral      37
Double-well potentials      19
Drag in not-so-slender bodies      149
Drag, effect of Mach number      145
Drag, transonic coordinates      146
Dynamical system      259 262
Eigensolutions to conservation laws      226 236
Eigenvalue problem      100 225 226 228 231 234
Elliptic boundary layer problems      55
Emden-Fowler equation      247 249
Energy considerations, Melnikov type      24 26—28
Energy dissipation      24
Energy, activation      254 256
Entropy condition, geometric      81
Euler equations      171
Evolution equations      175
Exchange of stability      262
Explosion      161
Extinction      109
Far fields as perturbations of sonic flow      153
Far fields in near-sonic flows      252
Far fields, asymptotics      99 104
Fast/slow system      5
Fermi Exclusion Principle      199
Finite difference methods, comparison with lattice Boltzmann methods      204
Finite difference methods, conditionally monotone      196
Finite difference methods, relationship to lattice gas methods      198
Flame propagation      100 108
Forward marching      48 50
Free boundary problem      254
Galerkin method, combined with perturbation techniques      113
Gasdynamic equations, detonation      171
Gasdynamic equations, interaction of shock and rarefaction      92
Gasdynamic equations, nozzle flow      229—236
Gasdynamic equations, simple shock      91
Geometric entropy condition      79
Geometry, differential      40
Geometry, phase-plane      3 12 13
Geostrophic initialization      143
Geostrophy, equations      142
Global decomposition      42
Godunov method      83 86 87 91
Group velocity      101
Heat equations, hyperbolic      222
Heat equations, nonlinear      217
Heterogeneous domain decomposition      137
Heterojunction devices, away from the solution      190
Heterojunction devices, bandgaps      186
Heterojunction devices, inner solution      188
Heterojunction devices, materials in      186
Heterojunction devices, outer solution      187
Heterojunction devices, simulation of      186
Homoclinic orbit      18
Hybrid perturbation-Galerkin method with domain decomposition      130
Hybrid perturbation-Galerkin method, application to problem involving compressible flow      122
Hybrid perturbation-Galerkin method, description      115
Hybrid perturbation-Galerkin method, example      117
Hybrid perturbation-Galerkin method, semi-analytical technique      128
Hybrid perturbation-Galerkin method, semi-numerical technique      128
Hybrid perturbation-Galerkin method, summary      114
Hyperbolic equations, in combustion      222
Induction equations      165
Induction flame      168 169 171
Induction Period      164
Induction time, constant-pressure      163 165
Initial boundary value problems for solving propagating flames problems      109
Initial boundary value problems in ocean modeling      140
Integrals, asymptotic evaluation of      60 62
Integrals, asymptotic expansion of      3 11
Kolodner — Coffman method      250
Laplace's method      101 102
Lattice Boltzmann methods, Chapman — Enskog analysis      202
Lattice Boltzmann methods, comparison with finite difference methods      203
Lattice Boltzmann methods, equations      201
Lattice Boltzmann methods, origin from lattice gas methods      198
Lattice gas automata      196
Lattice gas methods for fluid dynamics models      197
Lattice gas methods, collision operator      200
Lattice gas methods, collision rules      20
Lattice gas methods, conservation laws with      201
Lattice gas methods, microdynamical equation      199
Lattice gas methods, occupation number      199
Lattice gas methods, state transition function      200
Leading-order energy, definition      20
Leading-order energy, dissipation of      23
Leading-order energy, time evolution of      21
Lienard equation      3 8
Lienard plane      5 7 8
Lienard variable      5
Linear function, in boundary layer      48
Lyapunov functions      250
Macsyma      241
Maple      241—264
MAPLE, bifurcation analysis      254 258 262
MAPLE, changing variables with      249
MAPLE, comparison techniques with      250
MAPLE, introduction to      242—246
MAPLE, series solutions generated with      247
MAPLE, study of bifurcation phenomena in combustion      254
MAPLE, verifying conditions with      253
Marching, forward      50 52
Matching to transition region      28
Matching with asymptotic expansions      41 51 76 79 84
Mathematica      241
Mean occupation numbers      199
Melnikov-type energy considerations      24—26
Melting parameter      256
Microdynamical equation      197
Minimum viscosity method      84 89
Modeling, combustion      108 255
Modeling, detonation      173
Modeling, ocean      139—140 143
Molecular chaos      198
Monotonicity, conditions of      200
Multiple point combustion      255
Multiple scales method      20
Multiple scales problems, accuracy improved with asymptotic analysis      75
Multiple scales problems, domain decomposition methods with      34
Multiple scales problems, ocean models      139
Multiple scales problems, variation with      34
Navier — Stokes equations      100 102 107 198
Neutral stability curve      258
Not-so-slender bodies      148 149
Nozzle flow, gasdynamic equations      226
Nozzle flow, inviscid case      229 231
Nozzle flow, viscous case      230
Numerical computation, comparison with matched asymptotics      53
Occupation number      199
Ocean modeling      139—140 143
Orthogonal polynomials      47
Oscillation of second-order equations      250
Oscillation, capture of      25 29
Parabolic boundary layer problems      59
Parabolic equations, higher order      219
Parabolic layers      59 62 63 77
Parallel computation, with domain decomposition      33
Perturbation techniques for solutions to PDEs      114
Perturbation techniques for sonic flow problems      151
Perturbation techniques with Galerkin method      113
Perturbation techniques, dissipative      17 19
Perturbations, singular      3—16
Phase condition      110
Phase front      256 259
Phase-plane geometry      3 12 13
Planar traveling waves      109
Polynomials, orthogonal      47
Preuss's method      43 45
Propagation of combustion front      255
Propagation, theory      100
Pulsating waves      259
Pulses, solitary      26 27
Quantum Liouville equation for large heterojunction devices      186
Quantum Liouville equation for small analog devices      186
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