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Ames W.F. — Numerical methods for Partial Differential Equations
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Название: Numerical methods for Partial Differential EquationsАвтор: 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.
Язык: Рубрика: Математика /Численные методы /Численный анализ /Статус предметного указателя: Готов указатель с номерами страниц ed2k: ed2k stats Издание: Second EditionГод издания: 1977Количество страниц: 367Добавлена в каталог: 18.02.2005Операции: Положить на полку |
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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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