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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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Longley, H. J. 217 228 239 312 Lowan, A. N. 194 228 Lower bounds, for nonlinear parabolic equations 339—342 Lozenge see “Computational molecules” Ludford, G. S. S. 267 315 Lumped parameter problem 98 Lynch, R. E. 157 164 Lyusternik acceleration, relaxation form 119 Lyusternik, L. A. 119 162 Macagno, E. O. 289 317 Mackenroth, E. 259 314 Madsen, N. K. 304 319 Magneto-gas dynamics 270 Mann, W. R. 247 312 Manohar, R. 283(151) 316 Marching problems 5 Marchuk, G. 309 319 Marker and cell method, for Navier — Stokes equations 291—294 Marker and cell method, for Navier — Stokes equations, algorithms 292—294 Marker and cell method, for Navier — Stokes equations, instability 291 Marker and cell method, for Navier — Stokes equations, net 292 Marker and cell method, for Navier — Stokes equations, particles 293 294 Markhoff, W. 140 163 Martin, H. C 320(9) 348 Martin, R. E. 302(201a) 318 Martin, S. C 227(51) 229 Massau. J. 181 Matrix, consistent 120 Matrix, diagonal dominance 102 Matrix, nilpotent 108 Matrix, ordering 120—122 Matrix, property (A) 120 Matrix, reducible 104 Matrix, sparse 98 Matrix, Stieljes 150 Matrix, symmetric 109 Matrix, tridiagonal 151 Max norm 196 Maximum modulus theorems 93 Maximum principle for parabolic equations 337—340 Maximum principle in error analysis 44 McGuire, G. R. 222 225 229 McHenry, D. 320 348 Membrane eigenvalue problem 246 247 Mesh, point ordering 105 Mesh, refinement 214 Mesh, region 276 Method, characteristics 3 170 Method, explicit 193—196 Method, lines 3 302—304 Method, natural 3 Metropolis, N. C. 263(93) 314 Meyer, H. A. 300 301 318 Midpoints application 205 Mikeladze, Sh. 30 40 Mikhlin, S. G. 304 319 333 335 336 349 350 Miller, E. L. 87 91 Milne, W. E. 15 40 46 90 233 234 311 Milne-Thompson, L. M. 20 40 Mitchell, A. R. 156 157 163 164 255 313 Mitrinovic, D. S. 339 350 Mixed systems 270—274 Modulus of precision 26 Moments, method of 323 Momentum equations, conservation form 291 Monte Carlo methods 299—302 Monte Carlo methods, difference equations 300 302 Monte Carlo methods, random walk 300 301 Moon, P. 3 39 46 90 246 312 Morawetz, C. S. 263 315 Morimoto, H. 271 272 315 Morris, J. 219 221 225 226(49) 229 265 315 Morton, K.W. 200 208 211 215 224(18) 228 228 238 239 242 260 263 265 272 312 Moser, H. 159 164 Motz, H. 234 235 250 311 313 Moving threadline equations 176 Nagumo — Westphal lemma 339 Nagumo, M. 339 350 Natural finite difference, for parabolic equations 50 Natural methods 3 Navier — Stokes equations 281—299 Navier — Stokes equations, Boussinesq approximation 282 Navier — Stokes equations, exact solution 282 Navier — Stokes equations, momentum 284 Navier — Stokes equations, primitive variable methods 283 291—294 Navier — Stokes equations, stream function-vorticity methods 283—291 Navier — Stokes equations, vector potential methods 283 294—298 Network, choice of 33 34 Neumann problem 94 Newmark, N. M. 320 348 Newton method 259 Nicolson, P. 50 70 91 Ninham, B. W. 300 302 318 Noble, B. 283(151) 316 Noh, W. F. 263 315 Non-Newtonian fluids 159 Nonlinear elliptic equation 90 Nonlinear elliptic equation, nonlinear over-relaxation 258 Nonlinear examples, heat conduction 159 Nonlinear examples, magnetostatics 159 Nonlinear examples, turbulent free convection 159 Nonlinear over-relaxation for elliptic equations 256—259 Nonlinear over-relaxation, applications 258 Nonlinear parabolic equations, Crank — Nicolson method 84 85 Nonlinear parabolic equations, predictor-corrector methods 85—88 Nonlinearity, nature of 261 Nonuniform mesh, irregularly shaped regions 275 Nonuniform mesh, mesh point 277 Norm 115 333 Norm, Euclidean 115 Norm, spectral 115 Normal derivative, approximation of by false boundary 33 Norrie, D. H. 342 350 Norton, H. J. 325 349 Notation, information suppressing 11 Number of iterations for convergence 114 118 Numerical methods survey (Giese) 282 Numerical procedure, natural 170 Oden, J. T. 320 320(14) 343 348 349 Oliger, J. 299 318 Operator, biharmonic 18 Operator, Laplace 18 Operator, positive 245 334 Operator, positive definite 245 334 Operator, vector Laplacian 296 Orcutt, G. H. 301 Order notation 2 Ordering, consistent 258 Ordering, points 125 Orszag, S. A. 299 307 318 319 Orthogonal collocation 325—329 Orthogonal functions 334 Orthogonal polynomials 326 Orthogonal polynomials, Chebyshev 326 Orthogonal polynomials, Hermite 326 Orthogonal polynomials, Laguerre 326 Orthogonal polynomials, Legendre 326 Oscillations, nonlinear string 10 Ostrowski, A. M. 113 162 249 313 Over-relaxation parameters, determination 134 Over-relaxation parameters, experimental 134 Over-relaxation parameters, optimum 123—125 Over-relaxation, nonlinear 256—259 Overlapping steps 55 Overstability, hyperbolic equations 197—199 O’Brien, G. G. 2 39 50 51 91 200 228 Padmanabhan, H. I. 131 162 Padmanabhan, M. 227 229 283 294 317 Parabolic equations 4 64 Parabolic equations, alternating direction 252—255 Parabolic equations, explicit method 42—46 Parabolic equations, generalization of elementary methods 251 252 Parabolic equations, implicit method 42 Parabolic equations, reducible error 69 Parabolic equations, several space variables 251—255 Parabolic equations, variable coefficients 65 Parameter, relaxation 106 Parter, S. V. 274 315 Payne, R. B. 217 228 283 284 316 Peaceman — Rachford method 151 Peaceman, D. W. 52(25) 91 149 150 151 154 163 252 313 Pearcy, C. 156(71) 163 255(56) 255 313 Pearson, C. E. 290 294 317 Phillip, J. R. 159 164 Phillips, H. B. 1 39 Phillips, N. A. 260 314 Physical problems, classification 3—5 Pian, T. H. H. 344 350 Plane strain 275 Plane stress 275 plasma 271 Plastic bar, compression 10 192 Pogorelov, A. V. 260 314 Pohlhausen, K. 323 349 Point iterative methods, convergence rates 107 144 Point iterative methods, Gauss — Seidel (single steps) 104 Point iterative methods, gradient method 135 136 Point iterative methods, Richardson 136 Point iterative methods, semi-iterative 139—143 Point iterative methods, simultaneous displacements (total steps) 103 Point iterative methods, successive displacements (single steps) 105 Point iterative methods, total steps (Jacobi method) 103 Pointwise stability 198 Poisson equation 97 Poisson equation for pressure 291 Poisson equation, Fourier analysis cyclic reduction 306 307 Poisson equation, interior singularity 232 Poisson equation, scalar 297 Poisson equation, vector 297 Poisson — Euler — Darboux equation 180 Polynomials, Chebyshev 137 326 Polynomials, Hermite 326 Polynomials, Laguerre 326 Polynomials, Legendre 326 Polytropic gas 268 Positive definite operator 112 114 334 Positive operator 112 334 Potential scalar 295 Potential vector 295—298 Potential, quasi- 295 296 Power method 248 249 251 Power method, convergence 248 249 Power method, properties 248 Prager, M. 277(136) 316 336(48) 350 Prager, W. 320 348 Prandtl, L. 97 161 Predictor-corrector, unconditional stability 88 Pressure equation 284 Pressure equation, Poisson form 291 Priestly, C. H. B. 159 164 Primitive variable method, marker and cell 291—294 Propagation problems 3 Properly posed problems 263 Property (A) 258 Protter, M. H. 336 337 350 Pseudoviscosity 222 240 241 244 Pujol, A. 283 289 294 317 Putre, H. A. 291 318 Quasilinear elliptic equation, semi-explicit technique 259 Quasilinear equations 42 167 Quasilinear equations, first-order 5 Quasilinear equations, parabolic 84 Quasilinear equations, second-order 7 Quasilinear equations, stress wave propagation 177 Quasilinear system 170—175 Quasilinear system, canonical equations 171 173 174 Quasilinear system, characteristics 173 Quasilinear system, normal form 173 Quasipotential 295 Quasipotential, existence of 296 Quenching, nonlinear parabolic equation 339 Quenching, nonlinear parabolic equation, approximate solution for 339—342 Quenching, nonlinear parabolic equation, upper and lower bounds 340—342 Rachford, H. H. 52(25) 91 149 150 153 154 163 252 255 313 Random numbers, generation 301 Random walk 300 301 Rate of convergence 114—118 Rate of convergence, average 137 Rate of convergence, best 110 Rayleigh, 3rd Baron (Strutt, J. W.) 324 349 Real gas, transonic flow 10 Reducible system 10 181 265 Rees.M. 209(28) 211(28) 214(28) 219(28) 228 Reich, E. 113 162 Reid, J. K. 125 164 Relaxation 2 Relaxation factor, variable 141 Relaxation, over- 98 Relaxation, under- 98 Research journals, numerical analysis 1 299 Rice, J. D. 52(25) 91 Rice, J. R. 157 164 Richardson, D. J. 263 314 Richardson, L. F. 1 2 5 39 55 91 136 137 163 247 313 Richardson’s method, application 138 Richardson’s method, convergence rate 138 Richardson’s method, round-off errors 138 Richtmyer, R. D. 29 40 46 56 59 62 73 74 90 200 207 208 211 215 219 220(18) 224(18) 228 239 242 260 264 265 272 312 315 Riemann invariants 179 180 266 268 Rigler, A. K. 125 164 275(133) 316 Riley, J. D. 249(46) 313 Rimon, Y. 290 318 Ritz method see “Stationary functional method” Ritz, W. 324 349 Rivlin, A. M. 301(202) 318 Roache, P. J. 283 287 288 289 291 294 299 317 Rosenberg, R. L. 111 162 Rosenhead, L. 77 91 Ross, L. L. 290(179) 318 Round-off error, analysis by probability 25—28 Rounding, even rule 27 Rudge, C. 1 Rutherford, D. E. 59 91 Rutishauser, H. 275(130) 316 Sakurai, A. 283(151) 316 Samarskii, A. A. 283 317 Sauer, R. 183 228 Scalar product 333 Schechter, S. 256 313 Schlichting, H. 77 91 Schmidt, E. 2 39 Schulz, W. D. 241 263 312 314 Secrest, D. 326 349 Seidel, L. 104 112 162 Semi-implicit method of Chorin 294 Semi-iterative method, average convergence rate 141 Semi-iterative method, cyclic Chebyshev 142 143 Semi-iterative method, symmetric successive over-relaxation 143 Separation of variables, for partial difference equations 46 250 Serrin, J. 159 164 Shannon, J. P. 291(182) 318 Shapiro, A. H. 8 39 Shaw, F. S. 33 40 Sheldon, J. 143 163 Shell analysis, finite differences 274 Shocks 212 238 Shortley, G. H. 30 40 137 163 Simple waves 185 186 188 Simple waves, centered 188 Simpson, J. H. 77 91
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