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Miller J.J.H. (ed.) — Singular Perturbation Problems in Chemical Physics: Analytical and Computational Methods
Miller J.J.H. (ed.) — Singular Perturbation Problems in Chemical Physics: Analytical and Computational Methods



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Íàçâàíèå: Singular Perturbation Problems in Chemical Physics: Analytical and Computational Methods

Àâòîð: Miller J.J.H. (ed.)

Àííîòàöèÿ:

Presents the work of leading Russian researchers in English for the first time. Explains the matching method for asymptotic solutions in chemical physics problems, overviews the theory and application of asymptotic approximations for problems in chemical physics governed by either ordinary or partial differential equations with boundary and interior layers, and relates numerical methods for singularly perturbed boundary value problems modeling diffusion processes. Includes sample problems and solutions. For researchers in chemical physics.


ßçûê: en

Ðóáðèêà: Ôèçèêà/

Ñòàòóñ ïðåäìåòíîãî óêàçàòåëÿ: Ãîòîâ óêàçàòåëü ñ íîìåðàìè ñòðàíèö

ed2k: ed2k stats

Ãîä èçäàíèÿ: 1997

Êîëè÷åñòâî ñòðàíèö: 373

Äîáàâëåíà â êàòàëîã: 05.12.2009

Îïåðàöèè: Ïîëîæèòü íà ïîëêó | Ñêîïèðîâàòü ññûëêó äëÿ ôîðóìà | Ñêîïèðîâàòü ID
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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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