Page 7 - Numerical methods for chemical engineering

Contents

Preface page ix

1 Linear algebra 1
Linear systems of algebraic equations 1
Review of scalar, vector, and matrix operations 3
Elimination methods for solving linear systems 10
Existence and uniqueness of solutions 23
The determinant 32
Matrix inversion 36
Matrix factorization 38
Matrix norm and rank 44
Submatrices and matrix partitions 44
Example. Modeling a separation system 45
Sparse and banded matrices 46
MATLAB summary 56
Problems 57

2 Nonlinear algebraic systems 61
Existence and uniqueness of solutions to a nonlinear algebraic equation 61
Iterative methods and the use of Taylor series 62
Newton’s method for a single equation 63
The secant method 69
Bracketing and bisection methods 70
Finding complex solutions 70
Systems of multiple nonlinear algebraic equations 71
Newton’s method for multiple nonlinear equations 72
Estimating the Jacobian and quasi-Newton methods 77
Robust reduced-step Newton method 79
The trust-region Newton method 81
Solving nonlinear algebraic systems in MATLAB 83
Example. 1-D laminar flow of a shear-thinning polymer melt 85
Homotopy 88
Example. Steady-state modeling of a condensation
polymerization reactor 89

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