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| Авторизация |
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| Поиск по указателям |
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| Shaw F.S. — Relaxation methods |
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| Предметный указатель |
Accuracy, difference corrections 313 314
Accuracy, differencing as guide to 67
Accuracy, general 311
Accuracy, improving by use of finer mesh 185
Accuracy, improving finite difference representation 312
Accuracy, increasing 14
Accuracy, integral equations 306
Accuracy, ordinary differential equations 63
Algebraic equations, linear simultaneous 7
Axisymmetric problems, infinite regions 150
Axisymmetric problems, second order partial differential equations, approximation to relaxation operator 154
Axisymmetric problems, second order partial differential equations, boundary conditions 152
Axisymmetric problems, second order partial differential equations, discrepancies due to coarse mesh 160
Axisymmetric problems, second order partial differential equations, incorrect relaxation operator 156
Axisymmetric problems, second order partial differential equations, irregular stars 166
Axisymmetric problems, second order partial differential equations, residual and relaxation operators 153
Bickley, W.G. 42
Biharmonic equation 196 223
Biharmonic equation, boundary conditions 199 230
Biharmonic equation, fictitious points 199
Biharmonic equation, group relaxation 219
Biharmonic equation, line and block relaxation operators 208
Biharmonic equation, residual and relaxation operators 197
Biharmonic operator, boundary conditions 230
Biharmonic operator, curved boundaries and irregular stars 223
Biharmonic operator, finite difference approximations 38 39
Biharmonic operator, irregular star second derivatives 231
Biharmonic operator, iteration 225 226 227
Biharmonic operator, multiply- connected regions 223
Biharmonic operator, selvedge points 224 227
Block 105
Block operators 5
Boundary conditions, axisymmetric second order partial differential equation 152
Boundary conditions, biharmonic equation 199 230
Boundary conditions, displacement, curved boundaries, Poisson’s equation 113
Boundary conditions, displacement, multiply-connected region, Laplace's equation 139
Boundary conditions, iteration, Poisson’s equation 117
Boundary conditions, line integral, Poisson’s equation 141 143
Boundary conditions, line integral: Laplace’s equation 129
Boundary conditions, normal derivative, Laplace’s equation 128 129 138
Boundary conditions, plane stress problems 192
Boundary conditions, two simultaneous second order partial differential equations 168 177
Build-up process 47
Coarse mesh 74
Colin, E.C. 143 144
Constraint 2 3
Constraint, forces on 3
Convergence 21
Convergence, slowing down 14
Convergence, speeding up 10
Crout, P.D. 24
Curved boundaries, biharmonic operator 223
Curved boundaries, irregular star operators 113
Curved boundaries, Laplace’s equation 138
Curved boundaries, partial differential equation eigenvalue problems 272
Curved boundaries, Poisson’s equation, fictitious points 126
Curved boundaries, Poisson’s equation, graphical treatment 116
Curved boundaries, Poisson’s equation, irregular star operators 113 114 115 116 126
Curved boundaries, Poisson’s equation, linear relaxation operators 115
Curved boundaries, Poisson’s equation, second degree polynomial operators 117 119
Curved boundaries, two simultaneous second order partial differential equations 183
Difference corrections, accuracy 313 314
Differencing as guide to accuracy 67
Differential equations, linear ordinary 46
dimensions 320
Displacement 2 11
Displacement increment 3 8
Displacement unit 4
Eigenfunctions, orthogonality properties 244 250
eigenvalue problems 233
Eigenvalue problems, Algebraic equations 233
Eigenvalue problems, Algebraic equations, modal elimination 243
Eigenvalue problems, Algebraic equations, relaxation operators 235
Eigenvalue problems, optimal synthesis 277
Eigenvalue problems, ordinary differential equations 249
Eigenvalue problems, ordinary differential equations, method of solution 251
Eigenvalue problems, ordinary differential equations, Rayleigh Quotient 250
Eigenvalue problems, partial differential equations 266
Eigenvalue problems, partial differential equations, curved boundaries 272
Eigenvalue problems, partial differential equations, Rayleigh Quotient 267
Electrical networks 25
Elliptic equations 71 72
Emmons, H.W. 116
Equation, biharmonic 196 223
Equation, Laplace’s 149
Equation, Poisson’s 150
Equations, differential, approximate finite difference solution 26
Equations, eigenvalue 233
Equations, eigenvalue, algebraic 233
Equations, eigenvalue, ordinary differential 249
Equations, eigenvalue, partial differential 272
Equations, elliptic 71 72
Equations, fourth order partial differential 196
Equations, hyperbolic 71 72
Equations, ill-conditioned 22
Equations, integral 299
Equations, linear algebraic simultaneous 7
Equations, linear ordinary differential 47
Equations, non-linear, free surface problems 283 284
Equations, parabolic 71 72
Equations, second order linear partial differential 149 167
Errors, finite difference approximations to ordinary derivatives 29
Errors, sources of, ordinary differential equations 66
Fictitious points, biharmonic equation 219
Fictitious points, curved boundaries and irregular stars 113 114 115 116
Fictitious points, two simultaneous second order partial differential equations 178 183
Finite-difference approximations 26
Finite-difference approximations, biharmonic operator 38 39
Finite-difference approximations, error involved 29
Finite-difference approximations, improvements 312
Finite-difference approximations, integrals 41 42 43
Finite-difference approximations, Laplace operator, Cartesian coordinates 38 40 41 107
Finite-difference approximations, Laplace operator, rotational symmetry 38 40
Finite-difference approximations, linear ordinary differential expressions 33
Finite-difference approximations, linear partial differential expressions 38
Finite-difference approximations, ordinary derivatives, polynomial representation 29 31
Finite-difference approximations, ordinary derivatives, simple derivation 27
Finite-difference approximations, ordinary derivatives, Taylor series 29
Finite-difference approximations, partial derivatives, hexagonal and triangular meshes 40
Finite-difference approximations, partial derivatives, more correct expressions 41
Finite-difference approximations, partial derivatives, shift operator 37
Finite-difference approximations, partial derivatives, square mesh 33 34
Finite-difference approximations, Poisson’s equation 74
Forces, on constraints 3
Fourth order linear partial differential equations 196
Fox, L. 21 23 126 137 138 224 226 227 312 313 320
frameworks 1 25
Free surface problems 281
Free surface problems, Elasto-plastic torsion problem 281
Free surface problems, non-linear differential equation 283 284
Free surface problems, relaxation-iteration procedure 285 299
Girders 24
Graphical treatment, curved boundaries, Poisson’s equation 116
Group relaxation operators 19 21
Group relaxation, biharmonic equation 219
Hexagonal mesh 40
Howard, W. 178
Hyperbolic equations 71 72
Ill-conditioned equations 22
Increments of displacement 3 8
Infinite regions, axisymmetric problems 150
Infinity, position of 152
Instability, strut, non-dimensional treatment 323
Integral equations 299
Integral equations, accuracy 306
Integral equations, residual and relaxation operators 301
Integrals, finite difference approximations 41 42 43
Irregular stars, axisymmetric problems 166
Irregular stars, biharmonic operator 223 231
Irregular stars, curved boundaries 113 114 115 116
| Irregular stars, first derivative expressions 325
Irregular stars, tables, first derivative coefficients 328
Irregular stars, tables, fourth derivative coefficients 372
Irregular stars, tables, second derivative coefficients 350
Iteration, biharmonic equation 225 226 227
Iteration, free surface problems 285 299
Iteration, Poisson’s equation 117 142
Laplace operator, finite-difference approximation 38 40 41
Laplace’s equation 106 149
Laplace’s equation, block relaxation 109
Laplace’s equation, finite-difference approximation 107
Laplace’s equation, line integral boundary condition 129
Laplace’s equation, lines of symmetry 107
Laplace’s equation, multiply-connected region, displacement boundary condition 139
Laplace’s equation, normal derivative boundary condition 128 129
Laplace’s equation, normal derivative boundary condition, strings 138
Laplace’s equation, residual and relaxation operators 107
Laplace’s equation, special symmetry operators 108
Line relaxation operators 56
Liquidation of residuals 3 10 55
Loading term, Poisson’s equation 186
Localized fine mesh 186
Magnitude of unit block 105
Maxwell reciprocal relations 21
Mesh, coarse 74
Mesh, coarse, axisymmetric problem fine localized 186
Mesh, hexagonal 40
Mesh, mixed, special operators, Poisson’s equation 187 190
Mesh, refining of 66 185
Mesh, square 34
Mesh, triangular 40
Modal elimination, eigenvalue problems 243
Morris, J. 24
Multiply-connected region, biharmonic operator 223
Multiply-connected region, Laplace’s equation 139
Multiply-connected region, Poisson’s equation 139
Networks, electrical 25
Neville, E.H. 24
Newmark, N.M. 143 144
Non-dimensional treatment 320 321 323
Operators, block 5
Operators, displacement 5
Operators, irregular star 113 115 117 119 126 325 328 350 372
Operators, relaxation 5 7 11 17
Operators, relaxation, algebraic eigenvalue problems 235
Operators, relaxation, approximation to 154
Operators, relaxation, biharmonic equation 197
Operators, relaxation, block, biharmonic equation 208
Operators, relaxation, block, Poisson’s equation 84 87
Operators, relaxation, group 19 21 219
Operators, relaxation, handle of 17
Operators, relaxation, incorrect, use of 156
Operators, relaxation, integral equations 301
Operators, relaxation, Laplace’s equation 7
Operators, relaxation, line, biharmonic equation 208
Operators, relaxation, line, ordinary differential equations 56
Operators, relaxation, line, Poisson’s equation 84 86
Operators, relaxation, ordinary differential equations 49
Operators, relaxation, ordinary differential equations, eigenvalue problems 252—257
Operators, relaxation, partial differential equations, eigenvalue problems 268 269
Operators, relaxation, partial differential equations, two simultaneous 170 182
Operators, relaxation, symmetry 95 108
Operators, relaxation, tuning up 17
Operators, relaxation, unit 11 17
Operators, relaxation, unit, axisymmetric problems 153 154
Operators, relaxation, unit, Poisson’s equation 75 77
Operators, relaxation, wedge 61
Operators, residual 7 12
Operators, residual, axisymmetric problems 153
Operators, residual, biharmonic equation 197
Operators, residual, integral equations 301
Operators, residual, Laplace’s equation 107
Operators, residual, ordinary differential equations 49
Operators, residual, Poisson’s equation 75 77
Operators, residual, two simultaneous second order partial differential equations 170 182
Operators, special, mixed meshes, Poisson’s equation 187 190
Operators, special, symmetry, Laplace’s equation 108
Optimal synthesis 277
Ordinary derivatives, finite-difference approximations 27 29 31
Ordinary differential equations, accuracy 63
Ordinary differential equations, reduction to finite-difference equations 47
Ordinary differential equations, relaxation operators 49 56
Ordinary differential equations, residual operators 49
Ordinary differential equations, sources of error 66
Ordinary differential equations, terminal conditions 69
Ordinary differential expressions, finite-difference approximations 33
Orthogonality of eigenfunctions 244 250
Over-relaxation 14 21 55 156
Parabolic equations 71 72
Partial derivative expressions, finite-difference approximations 38
Partial derivatives, finite-difference approximations 33
Plane stress problem, boundary conditions 192
Poisson’s equation 72 73 96 150
Poisson’s equation, block relaxation operators 84 87
Poisson’s equation, boundary conditions, iteration 117
Poisson’s equation, curved boundaries and irregular stars 113 114 115 116 117 119 126
Poisson’s equation, displacement boundary condition 113
Poisson’s equation, fictitious points 126
Poisson’s equation, finite-difference approximation 74
Poisson’s equation, line relaxation operators 84 86
Poisson’s equation, loading term 186
Poisson’s equation, multiply-connected region 139 141 142 143
Poisson’s equation, residual operator 75 77
Poisson’s equation, special operators for mixed meshes 187 190
Poisson’s equation, unit relaxation operator 75 77
Quadratic function, positive definite 21
Rayleigh quotient 250 267
Reciprocal relations, Maxwell 21
Refining meshes 66
Relaxation operators 5 7 11 17
Relaxation operators, algebraic eigenvalue problems 235
Relaxation operators, approximation to 154
Relaxation operators, biharmonic equation 197
Relaxation operators, block, biharmonic equation 208
Relaxation operators, block, Poisson’s equation 84 87
Relaxation operators, group 19 21 219
Relaxation operators, handle of 17
Relaxation operators, incorrect, use of 156
Relaxation operators, integral equations 301
Relaxation operators, Laplace’s equation 107
Relaxation operators, line, biharmonic equation 208
Relaxation operators, line, ordinary differential equations 56
Relaxation operators, line, Poisson’s equation 84 86
Relaxation operators, ordinary differential equations 49
Relaxation operators, ordinary differential equations, eigenvalue problems 252—257
Relaxation operators, partial differential equations, eigenvalue problems 268 269
Relaxation operators, symmetry 95 108
Relaxation operators, tuning up 17
Relaxation operators, unit 11 17
Relaxation operators, unit, axisymmetric problems 153 154
Relaxation operators, unit, Poisson’s equation 75 77
Relaxation operators, wedge 61
Relaxation, criterion for sufficiency of 14
Relaxation-iteration, free surface problems 285 299
Residual forces (residuals) 3 7
Residual operators 7 12
Residual operators, axisymmetric problems 153
Residual operators, biharmonic equation 197
Residual operators, integral equations 301
Residual operators, Laplace’s equation 107
Residual operators, ordinary differential equations 49
Residual operators, Poisson’s equation 75 77
Residual operators, two simultaneous second order partial differential equations 170 182
Residuals, checking of 22
Residuals, liquidation of 3 10 55
Residuals, smearing of 84
Residuals, washback of 56 84 88 117 143
Rotational symmetry, finite-difference approximation 38 40
Second order partial differential equations, rotational symmetry 149
Selvedge points 224 277
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