Page 9 - Numerical methods for chemical engineering

Contents vii

5 Numerical optimization 212
Local methods for unconstrained optimization problems 212
The simplex method 213
Gradient methods 213
Newton line search methods 223
Trust-region Newton method 225
Newton methods for large problems 227
Unconstrained minimizer fminunc in MATLAB 228
Example. Fitting a kinetic rate law to time-dependent data 230
Lagrangian methods for constrained optimization 231
Constrained minimizer fmincon in MATLAB 242
Optimal control 246
MATLAB summary 252
Problems 252

6 Boundary value problems 258
BVPs from conservation principles 258
Real-space vs. function-space BVP methods 260
The finite difference method applied to a 2-D BVP 260
Extending the finite difference method 264
Chemical reaction and diffusion in a spherical catalyst pellet 265
Finite differences for a convection/diffusion equation 270
Modeling a tubular chemical reactor with dispersion; treating
multiple fields 279
Numerical issues for discretized PDEs with more than two
spatial dimensions 282
The MATLAB 1-D parabolic and elliptic solver pdepe 294
Finite differences in complex geometries 294
The finite volume method 297
The finite element method (FEM) 299
FEM in MATLAB 309
Further study in the numerical solution of BVPs 311
MATLAB summary 311
Problems 312

7 Probability theory and stochastic simulation 317
The theory of probability 317
Important probability distributions 325
Random vectors and multivariate distributions 336
Brownian dynamics and stochastic differential equations
(SDEs) 338
Markov chains and processes; Monte Carlo methods 353
Genetic programming 362