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| Ïîèñê ïî óêàçàòåëÿì |
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| Miller J.J.H. (ed.) — Singular Perturbation Problems in Chemical Physics: Analytical and Computational Methods |
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| Ïðåäìåòíûé óêàçàòåëü |
Hot die-forming, numerical investigation of heat transfer 331—334
Hot rolling, diffusion modeling 334—359
Hot rolling, finite difference scheme 346—355
Hot rolling, heat transfer problem formulation 334—346
Hot rolling, numerical investigation of heat transfer 355—359
Hyperbolic equations, comer boundary layers 134
Hyperbolic partial differential equations, Vishik — Lyustemik method 118
Il'in, A.M. 4(5 8) 11(8) 45 309(14) 360(14) 361
Initial value problem, asymptotic algorithm 52—63
Initial value problem, boundary value problem, conditionally stable case 63—73
Initial value problem, passage to the limit 52—56
Initial value problem, small nonlinearity systems 74—79
Interior layers, contrast structures, overview 86—88
Interior layers, contrast structures, step-type contrast structures 99—100
Interior layers, critical cases, solution stability 111—113
Ivanova, A.N. 4(7) 45
Jordan matrices, corner boundary layers, parabolic equations 131—132
Kalachev, L. 61(5) 63(5) 80(5) 100(5) 105(5) 134(31) 165(45) 178—179
Kalyakin, L.A. 4(9) 45
Karpukhin, O.N. 41(17) 46
Katcman, E.A. 12(13) 45
Khudyaev, S. 82(9) 155(40) 178—179
Kinetic parameters, first slow time scale, dimensionless variables 39—40
Knorre, D. 134(34) 179
Kolesov, Yu. 159(43) 179
Komissarov, V.D. 4(9) 45
Ladyzhenskaya, O.A. 253(10) 361
Laplace operators, diffusion modeling 183
Laplace operators, partial differential equations, noncritical step-type solutions 140—146
Leading order terms, asymptotic solutions 34—35
Levitckii, A.A. 2(1) 45
Liquid-phase chain oxidation, equations 12—15
Local coordinates, asymptotic solution, Vishik — Lyusternik method 113—115
Lyapunov functions, asymptotic approximations, initial value problem 53
Lyapunov functions, stationary solutions, boundary and interior layers 111—113
Lyusternik, L.A. 113(27) 116(27) 233(7—8) 179 361
Maizus, Z.K. 12(14) 46
Marchuk, G.I. 308(11) 328(20) 361
Maslennikov, S.I. 4(9) 45
Matching conditions, asymptotic solutions, explosive scale 31—34
Matching conditions, asymptotic solutions, fast time scale 17 25—27
Matching conditions, asymptotic solutions, overview 2—4
Matching conditions, asymptotic solutions, slow time scales 11—12 27—30
Miller, J.J.H. 309(13 15) 360(13 35—36 39) 361—362
Miller, V.B. 38(16) 42(20) 46
Mullarkey, E. 362
Nayfeh, A.H. 4(10) 45
Nefedov, N. 113(26) 146(37) 152(38) 179
Neumann boundary conditions, concentrated sources diffusion equations 289—293
Neumann boundary conditions, concentrated sources diffusion equations, numerical computations 301—308
Neumann boundary conditions, concentrated sources diffusion equations, special and classical finite difference schemes 297—300
Neumann boundary conditions, corner boundary layers, parabolic equations 128
Neumann boundary conditions, diffusion modeling, prescribed values 210—211
Neumann boundary conditions, partial differential equations, step-type contrast solutions 146
Neumann boundary conditions, prescribed diffusion fluxes, classical finite difference equations 255—270
Neumann boundary conditions, prescribed diffusion fluxes, mathematical formulation 251—255
Neumann boundary conditions, prescribed diffusion fluxes, special finite difference schemes 271—275 277—286
Nicolis, G. 105(19) 179
Nikitin, A. 97(10 12) 134(30) 178—179
Nikolaev, E.S. 191(2) 360
Nishiura, Y. 113(25) 179
Noncritical case, partial differential equations, step-type contrast solutions 141—146
Nonisothermal fast chemical reactions, corner boundary layers 134—139
Nonlinear problems, critical case 79—80
Nonzero corrections, asymptotic solutions, fast time scale 26—27
Normalized diffusion flux, concentrated sources, equations for 291—293
Normalized diffusion flux, concentrated sources, special and classical finite difference schemes 299—300
Normalized diffusion flux, diffusion modeling, boundary value problems, classical finite difference techniques 228—231
Normalized diffusion flux, diffusion modeling, overview 196—206
Normalized diffusion flux, heat transfer diffusion modeling, hot rolling 342—346
Normalized diffusion flux, prescribed diffusion fluxes, classical finite difference schemes 265—270
Normalized diffusion flux, prescribed diffusion fluxes, mathematical formulation 252—255
Novikov, E.A. 3(3) 45
Nowacki, W. 177(48) 179
O'Riordan, E. 309(15) 360(35—36) 361—362
Obukhova, L.K. 42(19) 46
One-dimensional (truncated) equation, thin body heat conduction 167
One-dimensional (truncated) equation, thin body heat conduction, diffusion modeling 184—191
One-dimensional (truncated) equation, thin body heat conduction, finite difference diffusion modeling 242—249
One-dimensional (truncated) equation, thin body heat conduction, special finite difference scheme 275—286
Parabolic systems, corner boundary layers 125—128
Parabolic systems, corner boundary layers, asymptotic solutions 128—134
Parabolic systems, diffusion modeling, computational techniques 203—206
Parabolic systems, diffusion modeling, concentrated sources, equations for 292—293
Parabolic systems, diffusion modeling, overview 183
Parabolic systems, step-type contrast structures 98—99
Parabolic systems, Vishik — Lyusternik method 117—118
Parameter size, asymptotic solutions, matching methods 4—12
Partial differential equations, contrast structures, Fisher's equation 154—155
Partial differential equations, contrast structures, phase transition models 152—154
Partial differential equations, contrast structures, spike-type solutions 148—152
Partial differential equations, contrast structures, step-type solutions, critical case 146—148
Partial differential equations, contrast structures, step-type solutions, noncritical case 139—146
Partial differential equations, diffusion modeling, classical finite difference techniques 212—231
Partial differential equations, diffusion modeling, overview 183—191
Partial differential equations, Vishik — Lyusternik method, asymptotic solutions 115 117—118
Partial differential equations, Vishik — Lyusternik method, boundary layer of asymptotic expansion 116—117
Partial differential equations, Vishik — Lyusternik method, local coordinates 113—115
Partial differential equations, Vishik — Lyusternik method, overview 113
Passage to the limit theorem, asymptotic approximations 54—56
Passage to the limit theorem, boundary value problem 63—73
Passage to the limit theorem, critical case, small nonlinear systems 74—79
Periodicity condition, partial differential equations, step-type contrast solutions, critical case 147—148
Petrov, A. 97(10 12) 178
Phase plane, partial differential equations, spike-type contrast solutions 150—152
Phase transitions, diffusion models, partial differential equations 152—154
Phase transitions, diffusion models, plastic shear heat transfer 313
Phase transitions, diffusion models, step-type contrast structures 97
Piecewise uniform grids, diffusion modeling, boundary value problems, one-dimensional problems 242—249
Piecewise uniform grids, diffusion modeling, boundary value problems, special construction principles 239—242
Plastic shear heat transfer, diffusion modeling 309—321
Plastic shear heat transfer, diffusion modeling, boundary value problems 313—315
Plastic shear heat transfer, diffusion modeling, heat exchange mechanisms 310—313
Plastic shear heat transfer, diffusion modeling, numerical investigation 315—321
Polyak, L.S. 2(1) 45
Pomeau, Y. 4(6) 45
Pontriagin, L. 77(7) 178
Postnikov, L.M. 41(17) 46
Prescribed diffusion fluxes, boundary value problems 249—286
Prigogine, I. 105(19) 179
Protter, M. 162(44) 179
Quasistationary concentrations, chemical kinetics, critical case equations 82—85
Ralph, S.K. 12(12) 45
Ratio table, boundary value problems 202—206
Reduced equations, boundary layers 49
Reduced systems, asymptotic algorithm 58—63
Reduced systems, initial value problem 52—53
Robin problems, diffusion modeling 210—211
Roginsky, V.A. 38(16) 42(20) 46
Romanovskii, Yu. 98(14) 178
Rubtsov, V.I. 38(16) 46
Rusina, I.F. 41(18) 46
Saddle points, boundary value problem, conditionally stable case 66—73
Saddle points, boundary value problem, contrast structures, overview 87—88
Saddle points, boundary value problem, contrast structures, spike-type contrast structures 102—104
Saddle points, boundary value problem, contrast structures, step-type contrast solutions 143—146
Saddle points, boundary value problem, contrast structures, step-type contrast solutions, second-order equations 94—97
Sakamoto, K. 113(24) 179
Samarsky, A.A. 191(1—2) 217(1) 308(1) 360
Sattinger, D. 166(46) 179
Scalar functions, chemical kinetics, contrast structures, second-order equations 86—88
Scalar functions, chemical kinetics, critical case equations 85
Scalar functions, chemical kinetics, critical case equations, initial value problem, small nonlinear systems 76—79
Schilders, W.H.A. 309(13) 360(13) 361
Scott, J.M.W. 12(12) 45
Second-order derivatives, corner boundary layers 126—127
Second-order derivatives, diffusion modeling, boundary value problems, finite difference techniques, special principles 243—249
Second-order derivatives, diffusion modeling, boundary value problems, overview 189—191
Second-order equations, spike-type contrast structures 101—104
Second-order scalar equations, contrast structures 86—88
| Second-order scalar equations, step-type contrast structures 88—97
Secular terms, asymptotic solutions, approximation formulas 7—8
Secular terms, asymptotic solutions, fast time scale 17 26—27
Secular terms, asymptotic solutions, first slow time scale 28—29
Semenov — Bodenstein method, chemical kinetics, critical case equations 82—85
Semiconductor theory, critical case methods 80—81
Separatrices, boundary value problem, conditionally stable case 66—68
Separatrices, boundary value problem, contrast structures, overview 87—88
Separatrices, boundary value problem, spike-type contrast structures 102—104
Separatrices, boundary value problem, step-type contrast structures 94—97
Shaidurov, V.V. 328(20) 361
Shanina, E.L. 42(20) 46
Shear line deformation, diffusion modeling, plastic shear heat transfer 310—312
Shishkin, G.I. 203(3—6) 215(4) 241(4) 309(4 15—19) 360(4 17—19 21—29 35—39) 360—362
Shlyapintokh, V.Ya. 41(17) 46
Shukurov, A. 97(11) 178
Shwetcova-Shilovckaya, T.N. 12(13) 45
Singular perturbation theory, autocatalytic reaction, overview 156—157
Singular perturbation theory, boundary value problems, boundary and interior layers 48—50
Singular perturbation theory, boundary value problems, classical finite difference scheme 255—270 300—308
Singular perturbation theory, boundary value problems, concentrated sources, diffusion equation 286—208
Singular perturbation theory, boundary value problems, conditionally stable case 64—73
Singular perturbation theory, boundary value problems, diffusion flux solutions 249—286
Singular perturbation theory, boundary value problems, finite difference techniques, classical and special experiments 300—308
Singular perturbation theory, boundary value problems, finite difference techniques, concentrated sources 294—300
Singular perturbation theory, boundary value problems, finite difference techniques, Neumann problem 271—275
Singular perturbation theory, boundary value problems, finite difference techniques, prescribed diffusion fluxes 211—249 275—286
Singular perturbation theory, boundary value problems, heat transfer applications 308—359
Singular perturbation theory, boundary value problems, heat transfer applications, hot die-forming heat transfer 321—334
Singular perturbation theory, boundary value problems, heat transfer applications, hot rolling heat transfer 334—359
Singular perturbation theory, boundary value problems, heat transfer applications, plastic shear heat transfer 309—321
Singular perturbation theory, boundary value problems, modeling diffusion 182—206
Singular perturbation theory, boundary value problems, numerical solutions for diffusion equations 206—249
Singular perturbation theory, chemical kinetics, critical case equations 82—85
Slow time scales, first scale, asymptotic solutions 17—20 27—29
Slow time scales, first scale, dimension variables 38—41
Slow time scales, second scale, asymptotic solutions 20—24 30—31
Slow time scales, second scale, dimension variables 41—43
Small nonlinearity, critical case, asymptotic algoritms 75—79
Small parameters, asymptotic solutions 2—4
Small parameters, asymptotic solutions, exclusion of 5—7
Small parameters, asymptotic solutions, fast time scale 17
Small parameters, liquid-phase chain oxidation equations 13—15
Small parameters, singularly perturbed differential equations 49—50
Sokoloff, D. 97(11) 178
Solonnikov, V.A. 253(10) 361
Southwell, R.V. 360(31) 361
Special finite difference techniques, concentrated source diffusion equations, numerical experiments 300—308
Special finite difference techniques, concentrated source diffusion equations, schemes for 294—300
Special finite difference techniques, diffusion modeling, boundary value problems, approximation errors 247—249
Special finite difference techniques, diffusion modeling, boundary value problems, construction principles, differential equations 233—242
Special finite difference techniques, diffusion modeling, boundary value problems, Dirichlet boundary condition 232—242 271—274
Special finite difference techniques, diffusion modeling, boundary value problems, finite difference principles 300—308
Special finite difference techniques, prescribed diffusion flux solutions, Neumann problem 271—275
Special finite difference techniques, prescribed diffusion flux solutions, numerical experiments 275—286
Spectrophotometry method (SPM), K7 and Ki determination 44—45
Spike-type contrast structures 101—110
Spike-type contrast structures, "brusselator" model 105—110
Spike-type contrast structures, boundary conditions 104—105
Spike-type contrast structures, partial differential equations 148—152
Spike-type contrast structures, second-order equations 101—104
Spike-type contrast structures, solutions 105
Spike-type contrast structures, solutions, stationary solutions 112—113
Stability, boundary and interior layers 111—113
Stationary solutions, boundary value problem, conditionally stable case 72—73
Stationary solutions, boundary value problem, critical cases, boundary and interior layers 111—113
Stationary solutions, boundary value problem, diffusion modeling 185—191
Steady-state concentrations, asymptotic solutions, approximation formulas 7—8
Steady-state concentrations, asymptotic solutions, fast time scales, dimension variables 38
Steady-state concentrations, asymptotic solutions, first slow time scale, dimension variables 41
Steady-state concentrations, asymptotic solutions, second slow time scale, dimension variables 42—43
Step with spike contrast structures 110
Step-type contrast structures 88—101
Step-type contrast structures, autonomous identities 100
Step-type contrast structures, fast and slow variables 97—98
Step-type contrast structures, multiple roots for equations 100—101
Step-type contrast structures, parabolic systems 98—100
Step-type contrast structures, partial differential equations, critical case solutions 146—148
Step-type contrast structures, partial differential equations, noncritical case solutions 139—146
Step-type contrast structures, phase plane cell 97
Step-type contrast structures, second-order equation 88—97
Step-type contrast structures, stationary solutions, boundary and interior layers 112—113
Sturm — Liouville problem, boundary and interior layers 111—113
Substance dissociation, diffusion modeling, thin body heat conduction 185—191
Summers, D. 12(12) 45
Sveshnikov, A. 54(2) 178
Taylor expansion, asymptotic solutions 5—6 22—24
Thermal diffusion coefficient, thin body heat conduction 175—177
Thermoelasticity, thin body heat conduction 177—178
Thin-body heat conduction, asymptotic approximation, boundary layer functions 172—174
Thin-body heat conduction, asymptotic approximation, construction 168—172
Thin-body heat conduction, diffusion modeling, overview 182—191
Thin-body heat conduction, diffusion modeling, plastic shear heat transfer 309—321
Thin-body heat conduction, overview 166—167
Thin-body heat conduction, small thermal diffusion coefficient 175—177
Thin-body heat conduction, thermoelasticity 177—178
Thin-body heat conduction, three-dimensional rod 174—175
Third boundary value problems, diffusion modeling 210—211
Three-dimensional rod, thin body heat conduction 174—175
Tihonov's theorem, initial value problem, asymptotic algorithm 56—63
Tihonov's theorem, initial value problem, passage to the limit 54—56
Tihonov's theorem, initial value problem, singularly perturbed differential equations 49—50
Tikhonov, A. 49(1) 52(1) 54(2) 178
Time scales, applications 35—45
Time scales, applications, chemiluminescence (CL) method 35—36
Time scales, applications, spectrophotometry method 36—37
Time scales, asymptotic solutions, explosive scale 31—34
Time scales, asymptotic solutions, overview 2—4
Time scales, asymptotic solutions, small parameters 24—25
Time scales, asymptotic solutions, steady-state concentration 7—8
Time scales, fast time scales 17 25—27
Time scales, fast time scales, dimension variables 37—38
Time scales, slow time scales, dimension variables 38—43
Time scales, slow time scales, first scale 17—20 27—29
Time scales, slow time scales, second time scale 20—24 30—31
Transition points, partial differential equations, spike-type contrast structures 104—105
Transition points, partial differential equations, step-type contrast solutions 142—146
Transition points, partial differential equations, step-type contrast structures 91—97
Trenogin, V. 118(28) 179
Uniform approximation, boundary layer function functions 51—52
Uniform approximation, corner boundary layers 127
Uniform approximation, diffusion modeling, boundary value problems, finite difference schemes 231—242
Uniform approximation, diffusion modeling, boundary value problems, hot die-forming procedures 332—334
Uniform approximation, diffusion modeling, boundary value problems, plastic shear heat transfer 316—321
Uniform approximation, diffusion modeling, boundary value problems, prescribed diffusion fluxes 260—270
Uniform approximation, diffusion modeling, boundary value problems, special finite difference, numerical examples 279—286
Uniform approximation, initial value problem, asymptotic algorithm 56—63
Uniform approximation, singularly perturbed differential equations 49—50
Ural'tseva, N.N. 253(10) 361
Urazgil'dina, T. 173(47) 178(49) 179
Van der Pol conditions, step-type contrast structures 98—99
Vasil'ev, V. 82(9) 98(14) 178
Vasil'eva, A.B. 12(11) 54(2—3) 60(4) 61(4—5) 63(5) 68—69(4) 74(4) 79(8) 80(5 8) 83(8) 85(8) 97(4 10 12) 99(15) 100(5) 101(16—17) 104(17) 105(5 18) 109(18) 110(18 20) 113(15—16 22—23) 45 178—179
Vector functions, critical case, initial value problem, small nonlinear systems 76—79
Vidal, C. 4(6) 45
Vishik — Lyusternik method, asymptotic approximations, boundary layers 116—117
Vishik — Lyusternik method, asymptotic approximations, local coordinates 113—115
Vishik — Lyusternik method, asymptotic approximations, overview 113
Vishik — Lyusternik method, asymptotic approximations, solutions 117—118
Vishik, M.I. 113(27) 116(27) 233(7—8) 179 361
Vol'pert, A. 82(9) 155(40) 178—179
Weinberger, H. 162(44) 179
Yakhno, V. 98(14) 178
Yanenko, N.N. 308(12) 361
Zeroth-order approximations, autocatalytic reaction models, leading term construction 158—161
Zeroth-order approximations, boundary value problem, conditionally stable case 65—73
Zeroth-order approximations, chemical kinetics, critical case equations 83—85
Zeroth-order approximations, corner boundary layers, nonisothermal fast chemical reactions 137—139
Zeroth-order approximations, initial value problem, asymptotic algorithm 60—63
Zeroth-order approximations, partial differential equations, step-type contrast solutions 143—146
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