Some Topics in Industrial and Applied Mathematics (Series in Contemporary Applied Mathematics)

Contents......Page 8
Preface......Page 6
1 Introduction......Page 10
2 Brouwer topological degree and the resolvent operator P......Page 12
3 Some existence results for finite variational inequalities......Page 18
4 The Poincare operator......Page 21
5 Periodic solutions......Page 23
6 Second order periodic dynamical system with friction......Page 33
References......Page 35
2 Complementarity Problems and Applications......Page 38
3 Verification of Solutions of Complementarity Problems......Page 40
4 Special Complementarity Problems......Page 44
5 Interval Data......Page 46
6 Newton’s Method......Page 49
8 Acknowledgement......Page 50
References......Page 51
Fernando Antoneli, Ana Paula S. Dias, Martin Golubitsky, Yunjiao Wang: Synchrony in Lattice Differential Equations......Page 52
1 Introduction......Page 53
2 Square Lattice with NN Coupling......Page 57
3 Square Lattice with NNN Coupling......Page 59
References......Page 64
1 Homogenization......Page 66
2 The periodic unfolding method[CDG]......Page 68
3 The unfolding operator......Page 69
4 Macro-Micro decomposition of functions......Page 71
5 Homogenization of nonlinear convex energies......Page 73
6 Homogenization of quasiconvex energies......Page 79
7 Homogenization of pointwise gradient constrained convex energies......Page 83
References......Page 85
1 Introduction......Page 87
2 Sparse matrices......Page 88
3 Direct Methods......Page 92
4.2 HSL......Page 95
4.3 Organization of HSL......Page 96
4.4 Development of HSL......Page 97
4.5 HSL code MA57......Page 98
4.7 HSL summary......Page 99
References......Page 102
Heinz W. Engl, Gerald Goekler, Andrea Schatz, Helmut Zeisel: Modelling and Numerics for the Transient Simulation of the Blast Furnace Process......Page 104
1 Introduction-a short description of the blast furnace process......Page 105
2.1 Modelling goals......Page 106
2.2 Gas flow......Page 107
2.3 Solid flow — a modified Bingham material approach......Page 108
2.5.1 Gas composition......Page 109
2.5.2 Solid material composition......Page 110
2.5.4 Temperature distribution of gas, solids and liquid......Page 111
2.5.5 Chemical reactions — Mass and heat sources......Page 112
3.2 Numerics of the gas flow......Page 113
3.3.1 Method of characteristics......Page 114
3.3.2 Incorporation of different time scales......Page 117
3.3.3 Fast and accurate approximation of balance equations — discretization of domain and equations......Page 118
3.3.4 Determination of the gas steady state with global subgrid-loops......Page 120
3.3.6 Incorporation of diffusion and wall heat loss......Page 121
3.4 The global iteration......Page 122
3.5 Results......Page 123
References......Page 127
1 Introduction......Page 129
2 The stage preceding the appearance of free boundaries......Page 131
3 Qualitative analysis of the problem with free boundaries......Page 134
4 Numerical simulations......Page 139
References......Page 141
1. Introduction......Page 143
2. Finding the optimal portfolio......Page 146
3. Martingale representation theorem......Page 149
4. Semi-continuous market model (discrete in time continuous in state)......Page 152
References......Page 160
1 Introduction......Page 161
2.1 Optimal stability......Page 163
2.2 Adaptive method construction......Page 164
3.2 1st order......Page 165
3.3 2nd order......Page 167
4 Maximal disk......Page 168
4.2 1st order......Page 169
4.3 2nd order......Page 170
4.4 3rd order......Page 171
5 Maximal imaginary interval......Page 172
5.2 1st and 2nd order......Page 173
6 Spectral gaps......Page 175
7 Maximal thin regions......Page 177
7.1 Algorithm......Page 178
7.2 Examples......Page 179
8.1 Semi-discrete advection-diffusion......Page 181
8.2 Optimal stability regions......Page 182
8.3 Method construction......Page 183
8.4 Numerical experiments......Page 185
9 Conclusion......Page 187
References......Page 188
1 Introduction......Page 190
2 Numerical schemes and MS-stability......Page 192
3 Two-dimensional MS-stability......Page 195
4 MS-stability of two-step methods......Page 197
References......Page 202
1 Introduction......Page 204
1.1 Discretizations......Page 205
2 Experiment I......Page 207
3 Experiment II......Page 209
4 Experiment III......Page 210
5 Conclusion......Page 212
References......Page 213
1 Introduction......Page 215
2 Examples of Subspace Approaches......Page 217
3 A model subspace algorithms......Page 220
4 Subspace Techniques for Constrained Optimization......Page 222
References......Page 226