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Ames W.F. — Numerical methods for Partial Differential Equations
Ames W.F. — Numerical methods for Partial Differential Equations

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Название: Numerical methods for Partial Differential Equations

Автор: Ames W.F.

Аннотация:

This volume is designed as an introduction to the concepts of modern numerical analysis as they apply to partial differential equations. The book contains many practical problems and their solutions, but at the same time, strives to expose the pitfalls — such as overstability, consistency requirements, and the danger of extrapolation to nonlinear problems methods used on linear problems. Numerical Methods for Partial Differential Equations, Third Edition reflects the great accomplishments that have taken place in scientific computation in the fifteen years since the Second Edition was published. This new edition is a drastic revision of the previous one, with new material on boundary elements, spectral methods, the methods of lines, and invariant methods. At the same time, the new edition retains the self-contained nature of the older version, and shares the clarity of its exposition and the integrity of its presentation.

Key Features
* Material on finite elements and finite differences have been merged, and now constitute equal partners
* Additional material has been added on boundary elements, spectral methods, the method of lines, and invariant methods
* References have been updated, and reflect the additional material
* Self-contained nature of the Second Edition has been maintained
* Very suitable for PDE courses


Язык: en

Рубрика: Математика/Численные методы/Численный анализ/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Издание: Second Edition

Год издания: 1977

Количество страниц: 367

Добавлена в каталог: 18.02.2005

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
Ablow, C. M.      258 314
Acceleration formula, Aitken      125
Acceleration formula, Lyusternik      119 125
Acceleration formula, successive over-relaxation (SOR)      119
Acoustic vibration as a mixed system      271
Ahamed, S. V.      260 (76) 314
Aitken, A. C.      125 162
Albasiny, E. L.      238 312
Aliasing      304 305
Allen, D. N. de G.      33 40
Alonso, C. V.      289 290 317
Alternating direction implicit methods (ADI)      148—157
Alternating direction implicit methods (ADI) for vorticity equation      289 290
Alternating direction implicit methods (ADI), comparison of convergence rates      157
Alternating direction implicit methods (ADI), double interlocking      149
Alternating direction implicit methods (ADI), Douglas — Rachford      149
Alternating direction implicit methods (ADI), higher dimensions      252 255
Alternating direction implicit methods (ADI), multistage      156 255
Alternating direction implicit methods (ADI), nonlinear parabolic equation      255
Alternating direction implicit methods (ADI), Peaceman — Rachford      149—151
Alternating direction implicit methods (ADI), stability      253
Alternating direction implicit methods (ADI), stationary      152
Alternating direction implicit methods (ADI), tridiagonal matrix      253
Alternating direction implicit methods, comparison      155 156
Alternating direction implicit methods, iteration parameters      154—156
Alternating direction implicit methods, optimum      156
Alternating direction implicit methods, Peaceman and Rachford      154
Alternating direction implicit methods, Wachspress      154
Ames, W. F.      6 7 9 37 39 40 42 73 74 76 77 78 79 89 90 91 98 131 132 134 161 162 175 176 177 179 202 203 227 229(51) 236 260 265 269 283(155) 312 315 317 319 320 321 348
Amsden, A. A.      294 318
Ansorge, R.      263 314
Approximate factorization method      309 310
Approximation, first-order      16
Approximation, Newton      132
Approximation, Picard      132
Approximation, second-order      17
Argyris, J. H.      320 348
Arms, R J.      106 145 162
Arnason, G.      261 314
Asymptotic meaning, for vectors      109
Asymptotics      10—14
Aziz, K.      283 289 291 294 295 298 317 318 320 343 348
Babuska, I.      277 316 336 350
Backward difference      22
Balance equation      260 261
Barber, M. N.      300 302 318
Basis functions, triangular      331
Batschelet, E.      33 40
Beams, large amplitude oscillations      281
Beckenbach, E. F.      339 350
Becker, M.      323 349
Bellman, R.      83 89 91 159 259 313 339 350
Berker, R.      281
Bernstein, D. L.      42 90 167 169 227
Bers, L.      256 313
Bickley, W. G.      15 40
Biezeno, C. B.      322 323 349
Biharmonic equation      250
Biharmonic equation, singularity in      232
Biharmonic equation, thirteen-point molecule      278
Binder, L.      2 39
Birkhoff, G.      35 40 149 150 152 153 154 156 163 275 316
Blackman, R.      305 319
Blair, A.      263 314
Bland, D. R.      265 315
Blasius solution      77
Block interative methods      144—148
Block interative methods, comparison of convergence rates      147
Block interative methods, Gauss — Seidel row iterations      145
Block interative methods, Jacobi row iteration      145
Block interative methods, single line      145
Block interative methods, successive over-relaxation by lines      146
Bodewig, E.      98 161 247 248 313
Boley, B. A.      339 350
Bolin, B.      261 314
Bolotin, V. V.      203 228
Boundary condition, dynamic      131
Boundary condition, finite element treatment      346
Boundary condition, internal      238
Boundary condition, kinematic      131
Boundary condition, mixed      150
Boundary condition, no-slip      286 298 299
Boundary layer      82
Boundary layer,equations      38 77
Boundary layer,flow      77
Boundary singularity      230 231
Boundary singularity, parabolic problem      231
Boundary value problems      3 4
Boundary vorticity production      287
Boundary, irregular      30—33
Boundary, irregular, Gerschgorin method      32 33
Boundary, irregular, Mikeladze method      30 31
Boundary, irregular, normal derivative      32
Boundary, sloping      79
Bradshaw, C. L.      247(35) 312
Bramble, J. H.      238 278 312 316
Brian, P. L. T.      254 313
Bridgman, P. W.      35 40
Brode, H. L.      241 312
Brown, G. W.      300 318
Bruce, G. H.      52 91
Bruhn, G.      262 314
Bubnov — Galerkin method      323 329—332
Bubnov — Galerkin method, equation residual      330
Bubnov — Galerkin method, initial residual      330
Bubnov — Galerkin method, relation to finite differences      331 332
Bubnov, I. G.      323 349
Burgers’ equation      76 84
Burgers’ equation, explicit solution      87
Burgers’ equation, predictor-corrector solution      87
Burstein, S. Z.      263 265 314 315
Burtness, R. D.      260(76) 314
Butter, D. S.      262 314
Callaghan, J. B.      275 316
Carre, B. A.      124 162
Carrier, G. F.      201 228
Carslaw, H. S.      35 40 42 90
Central difference      22
Chan, R. K.-C.      294 318
Chang, J. S.      304 319
Characteristics      5 266
Characteristics as natural coordinates      170 180
Characteristics for wave equation      165
Characteristics, complex      92
Characteristics, curved      190
Characteristics, direction      7
Characteristics, equations      7
Characteristics, method of      180—184 186
Characteristics, net      262
Charney, J. G.      260 314
Chebyshev polynomial, recurrence relation      140
Cheng, S. I.      290 318
Chorin, A. J.      216 228 283 294 316 318
Chorin’s method      294
Chu, B. T.      265 315
Clenshaw, C. W.      325 349
Clough, R. W.      320(9) 348
Coburn, N.      262 314
Cole, J. D.      88 91
Collatz, L.      2 3 31 39 40 44 90 107 118 162 194 228 247 281 313 316 323 333 336 349 350
Collocation      322
Collocation, orthogonal      325—329
Compatible method      see “Consistent method”
Completeness      333—338
Completeness in energy      335
Completeness in mean      335
Computational mesh, nonuniform      277
Computational molecules      15
Computational molecules, explicit for diffusion equation      44
Computational molecules, explicit-implicit for conservation laws      226
Computational molecules, nine-point for Laplace equation      127 128
Computational molecules, partial derivatives      17
Computational molecules, two-dimensional operators      18
Condition number (Todd)      137
Conservation form, Eulerian equations      216 239
Conservation form, momentum equations      291
Consistent method      61 62
Consistent method, conditions for      66
Consistent ordering, of matrix      120—122
Constant state      185 188
Contact discontinuity      238
Conte, S. D.      274 316
Convection, natural      294
Convergence      30 333—338
Convergence in energy      335
Convergence in mean      335
Convergence, average rate      137
Convergence, comparison of rates      128 129
Convergence, rates of      114
Cooley, J. W.      305 319
Coordinates, natural      170
Copley, D. T.      249 313
Corner, interior      234
Coupled equation method      278
Courant — Friedrichs — Lewy convergence, condition      222 224
Courant — Isaacson — Rees methods, first order equations      211 212 214
Courant, R.      1 39 41 90 167 173 179 184 194 205 209 211 212 214 219 227 228 238 240 245 246 262 265 312 314 315 320 323 348 349
Cox, J. G.      247(35) 312
Crandall, S. H.      29 40 48 49 55 71 77 91 113 162 182 228 231 246 249 280 311 312 313 316 323 336 349
Crank — Nicolson method      50 56
Crank — Nicolson method, alternating direction modification      254 255
Crank — Nicolson method, improvements      71
Crank — Nicolson method, parabolic equations      67
Crank — Nicolson method, relation to explicit-implicit method      226
Crank — Nicolson method, tridiagonal form      54
Crank — Nicolson method, two-dimensional problems      252
Crank — Nicolson method, von Neumann’s derivation      70
Crank, J.      42 50 91
Cryer, C. W.      160 164
Cuthill, E. H.      53 91 145 147 163
Daly, B. J.      291(182) 318
Dames, R. T.      274 316
De Bruijn, N. G.      10 40
de Vries, G.      343 350
Derivatives, difference approximations      20—23
Determinism, principle of      41
Diagonal dominance      110
Difference approximations, positive type for parabolic equations      65
Difference approximations, stability of      65—67
Difference equation for probability      300
Difference equation, unstable      55
Difference, backward      16
Difference, forward      16
Differential inequalities      339—342
Diffusion equation      2 271
Diffusion equation with chemical reaction      54 76
Diffusion equation, Cartesian form      35 36
Diffusion equation, circular cylindrical form      68
Diffusion equation, compared to Monte Carlo      300 301
Diffusion equation, Crank — Nicolson method      68
Diffusion equation, indeterminate form      68
Diffusion equation, line method for      303 304
Diffusion equation, spherical symmetric form      68 69
Diffusion equation, splitting method for      309
Diffusion equation, three-level formula      72
Dimensionless forms      34—36
Dirichlet problem      94
Discontinuity, evolution of      238
Discontinuity, propagation      8
Discretization, mathematical      15
Discretization, physical      15
Dispersive      242
Dissipative      242
Dissipative scheme, Kreiss sense      224
Divergence      41
Divergence form      see “Conservation form”
Dolph, C. L.      262 314
Domain of determinancy      204
Donovan, L. F.      291 318
Douglas — Rachford method (ADI)      151
Douglas — Rachford method (ADI), convergence rate      152
Douglas — Rachford method (ADI), spectral radius      152
Douglas, J.      44 45 53 71 72 73 82 83 84 89 90 91
Douglas, J., Jr.      72 85 86 91 133 149 151 153 156 158 163 164 252 254 289 313 317
DuFort and Frankel method      60
DuFort and Frankel method, applied to vorticity equation      289
DuFort, E. C.      61 91
D’Yakonov, Ye. G.      156 163
Ehrlich, L. W.      249 313
Eigenfunction      246
Eigenvalue problem      3 4 123 244—250
Eigenvalue problem, buckling of plate      245
Eigenvalue problem, inverse iteration      249
Eigenvalue problem, membrane problem      245
Eigenvalue problem, nonlinear      250
Eigenvalue problem, power method      248
Eigenvalue problem, self-adjoint      245
Eigenvalue problem, special      245
Eigenvectors, left      266
Eisen, D.      237 312
Elasticity, higher order equations      274—279
Elliptic equations, finite difference approximations      100—102
Elliptic equations, nonlinear      158—161
Elliptic equations, self-adjoint      102 149
Ellipticity condition, balance equations      260
Emmons, H. W.      284 317
Energy equation, Boussinesq approximation      282
Engli, M.      275(130) 316
Equations, along characteristics      181
Equations, classification      5-10
Equations, elliptic      7
Equations, hyperbolic      4 7
Equations, parabolic      4 7
Equations, reducible      10
Equations, thread line      9
Equilibrium problems      3 92
Equivalence theorem, John      66
Equivalence theorem, Lax      62
Erdelyi, A.      10
Erdelyi, E. A.      159(90) 164 234(4) 260 311
Error bounds      333—338
Error bounds for semilinear problems      336 337
Error distribution methods      see “Weighted residual methods”
Error, discretization      24
Error, mesh size relations      24
Error, reduction concepts      70—73
Error, round-off      24
Error, truncation      15 16 24
Euler, L.      1 39
Eulerian equations      212 213 216
Eulerian equations, conservation form      264
Eulerian equations, Courant — Isaacson — Rees method      214
Eulerian equations, Lax — Wendroff scheme      216—219
Eulerian equations, Leleviers scheme      215
Eulerian equations, plane motion      240
Eulerian equations, slab symmetry      218
Eulerian — Lagrangian coupled code      263
Euler’s method      1
Existence-uniqueness theorem, Cauchy — Kowalewski      93
Expected value      26
Explicit difference equations, improved      63 64
Explicit difference equations, molecules      52
Explicit difference equations, qualitative behavior      49
Explicit difference equations, two dimensions      251
Explicit method, hopscotch Lax scheme      222
Explicit method, nonlinear parabolic equations      73—76
Explicit method, nonlinear parabolic equations, example of      77-81
Explicit method, nonlinear parabolic equations, stability      73 74 80
Explicit method, second-order for conservation laws      225
Explicit-implicit methods for conservation laws      224-227
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