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Index
List of Tables
List of Figures
Preface - 1st Edition
Preface - 2nd Edition
Acknowledgements
1 Introduction
1.1 Introduction
1.2 Classification of chemical process models
1.3 Lumped parameter, steady state models
1.3.1 Example of a stagewise separation process
1.3.2 Process flow sheet simulation
1.3.3 Example of a multicomponent flas
1.3.4 Example of a phenomenalogical model
1.3.5 Example of reactors in series
1.4 Lumped parameter, dynamic models
1.4.1 Example of cooling a molten metal
1.4.2 Ozone decomposition
1.5 Distributed parameter, steady state models
1.5.1 Heat transfer through a tappered fin
1.5.2 Axial dispersion model
1.6 Distributed parameter, dynamic models
1.6.1 Heat transfer through a tappere
1.7 Putting it all together - Overview
1.7.1 Mathematical models and Physical laws
1.7.2 Mathematical models, numerical approximations and errors.
1.7.3 Algorithms
1.7.4 Errors in numerical computation
1.8 Summary
2 Single nonlinear algebraic equation
2.1 Introduction
2.2 Bisection method
2.3 Regula-falsi method
2.4 Newton’s method
2.5 Secant method
2.6 Müller’s method
2.7 Fixed point iteration
2.8 Error analysis and convergence acceleration
2.8.1 Convergence of the bisection method
2.8.2 Convergence of fixed point iteration method
2.8.3 Aetkins method for convergence acceleration
2.8.4 Convergence of the Newton’s scheme
2.9 Deflation technique
2.10 Software tools
2.10.1 MATLAB
2.11 Summary
2.12 Exercise problems
3 Review of Linear Algebra
3.1 Introduction
3.2 Matrix notation
3.2.1 Review of basic operations
3.3 Matrices with special structure
3.4 Determinant
3.4.1 Laplace expansion of the determinant
3.5 Vector and matrix norms
3.6 Condition of a Matrix
3.7 Direct methods
3.7.1 Cramers rule
3.7.2 Matrix inverse
3.7.3 Gaussian elimination
3.7.4 Thomas algorithm
3.7.5 Gauss-Jordan elimination
3.7.6 Gaussian elimination - Symbolic representaio
3.7.7 LU decomposition
3.8 Iterative methods
3.8.1 Jacobi iteration
3.8.2 Gauss-Seidel iteration
3.8.3 Successive over-relaxation (SOR) scheme
3.9 Gram-Schmidt orthogonalization procedure
3.10 The eigenvalue problem
3.10.1 Left and right eigenvectors
3.10.2 Bi-orthogonality
3.10.3 Power iteration
3.10.4 Inverse iteration
3.10.5 Shift-Inverse iteration
3.11 Summary
3.12 Exercise Problems
4 Systems of nonlinear algebraic equations
4.1 Newton’s method
4.1.1 Convergence test
4.2 Summary
4.3 Exercise Problems
5 Functional approximations
5.1 Approximate representation of functions
5.1.1 Series expansion
5.1.2 Polynomial collocation
5.2 Approximate representation of data
5.2.1 Approximation accuracy
5.3 Curve fitting
5.3.1 Least-squares approximation
5.4 General non-linear regression and linearization
5.4.1 Linearization
5.5 Difference operators
5.5.1 Operator algebra
5.5.2 Newton forward difference approximation
5.5.3 Newton backward difference approximation
5.6 Inverse interpolation
5.7 Lagrange polynomials
5.8 Newton’s divided difference polynomials
5.9 Piecewise continuous functions - spline
5.10 Exercise problems I
5.11 Numerical differentiation
5.11.1 Approximations for first order derivatives
5.11.2 Approximations for second order derivatives
5.11.3 Taylor series approach
5.12 Numerical integration
5.12.1 Romberg integration
5.12.2 Gaussian quadratures
5.13 Summary
5.14 Exercise Problems II
6 ODEs - IV
6.1 Model equations and initial conditions
6.1.1 Higher order differential equations
6.2 Taylor Series Methods
6.2.1 Explicit Euler scheme
6.2.2 Midpoint method - A modification of Eulers method
6.2.3 Implicit Euler scheme - Backward Euler
6.2.4 Modified Euler - Heun’s Method
6.2.5 Stability limits
6.2.6 Stiff differential equations
6.3 Runge-Kutta Methods
6.3.1 Explicit schemes
6.3.2 Euler formula revisited
6.3.3 A two-stage (v = 2) Runge-Kutta scheme
6.3.4 A fourth order Runge-Kutta scheme
6.3.5 Semi-implicit & implicit schemes
6.3.6 Semi-Implicit forms of Rosenbrock
6.4 Multistep methods
6.4.1 Explicit schemes
6.4.2 Implicit schemes
6.4.3 Automatic stepsize control
6.5 Summary
6.6 Exercise Problems
7 Boundary value problems
7.1 Finite difference method
7.1.1 Linear boundary value problem with constant coefficients
7.1.2 Linear boundary value problem with variable coefficients
7.1.3 Nonlinear boundary value problems
7.1.4 Parallel shear flow with constant dynamic viscosity (Newtonian fluid)
7.1.5 Parallel shear flow with velocity-dependent dynamic viscosity (non-Newtonian fluid
7.2 Shooting method fundamentals
7.3 Shooting method – linear and nonlinear problems
7.3.1 Linear problems
7.3.2 Nonlinear problems
7.4 Summary
7.5 Exercise Problems
8 Partial differential equations
8.1 Definitions
8.2 Elliptic Equations
8.2.1 Backward differentiation
8.2.2 Central derivatives and fictitious points
8.3 Parabolic equation
8.3.1 Fully-discrete methods
8.3.2 Semi-discrete methods
8.4 Hyperbolic equations
8.5 Summary
8.6 Exercise Problems
A MATLAB
A.1 Introduction
A.1.1 Introduction
A.2 Starting a MATLAB session
A.3 MATLAB basics
A.3.1 Using built in HELP, DEMO features
A.3.2 Data entry, line editing features of MATLAB
A.3.3 Linear algebra related functions in MATLA
A.3.4 Root finding
A.3.5 Curve fitting
A.3.6 Numerical integration, ordinary differential equations
A.3.7 Basic graphics capabilities
A.3.8 Producing printed output of a MATLAB session
A.3.9 What are m-files?
A.3.10 Programming features
B Number representation, significant figures and errors
B.1 Number Representation
B.1.1 Fixed point syste
B.1.2 Floating point system
B.2 Significant figures
B.3 Mathematical operations
B.3.1 Multiplication and Division
B.3.2 Addition and Subtraction
B.3.3 Multistep calculations
B.3.4 Multiplication / Division combined with Addition / Subtraction
B.4 Rounding and chopping
B.5 Taylor series expansion
B.6 Truncation errors
B.6.1 Big Oh notatio
B.7 Error propagation
B.8 Exercise problems
Bibliography
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