Chapter/Section Headings

Starting Page


Explanation
...Why nonlinear?
...Classification
...Nondimensionalization
...Advanced Classification of PDEs


Algebraic Equations
...Single Equation, MATLAB
...Single Equation, EXCEL
...Multiple Eq., MATLAB
...Linear Eq., MATLAB
...Linear Eq., EXCEL
...Linear Equations
...Successive Substitution, 1 var.
...Successive Substitution, many var.
...Newton-Raphson, 1 var.
...Newton-Raphson, many var.
...Convergence of SS
...Convergence of NR
...Critical Parameters
...Wegstein Method
...Process Simulators
...Advanced Topics
LU Decomposition
Matrix Structure
Tridiagonal Matrices
Arrow Matrix
Singular Value Decomposition
Inverse of a Matrix
Determinant
Conjugate Gradient
Homotopy & Continuation
Linear Difference Equatins
Eigenvalues


Interpolation
...Polynomials
...Orthogonal Polynomials
...Rational Polynomials
...Forward Differences
...Backward Differences
...Finite Elements
...Splines
...Errors
...Two Dimensions


Quadrature (integration)
...Analytic in Matlab
...Analytic in Mathematica
...Trapezoid Rule
...Trapezoid Rule with MATLAB
...Simpson's Rule
...Gaussian Quadrature
...Gaussian Quad., Matlab
...Spline
...Romberg's Method
...Singularities
...Errors


Initial Value Prob.(IVP)
...Terminology
...Solution by Quadrature
...Explicit Solution with MATLAB
...Theory of Explicit Methods
...Order of Method
...Extrapolation & Errors
...Step-size Adjustment
...Stability of Methods
...Stiffness
...Implicit Solution with MATLAB
...Implicit Methods
...Comparison
...Predictor-corrector methods
...Differential-Algebraic
...Computer Software
...Bifurcations
...Limit Cycles
...Sensitivity Analysis
...Equation solvers


Boundary ValueProb.(BVP)
...Analytic Soln. & Quadrature
Index
Solution by Quadrature
Solution by Power Series
Solution by Power Series
Problem II, Analytic
Problem II, Mathematica
Problem III, Analytic
Problem III, Mathematica
...Finite Difference
Index
Derivation
Analytic, Problem II
Mathematica, Problem II
Problem II, MATLAB
Problem II, EXCEL_Iter
Problem II, EXCEL2
Analytic, Problem III
Mathematica, Problem III
Problem III.Ver1, MATLAB
Problem III.Ver1, EXCEL
Problem III.Ver2, MATLAB
Problem III.Ver2, EXCEL
Problem III.Ver3, MATLAB
Problem IV, MATLAB SS
Problem IV, MATLAB NR
Problem IV, EXCEL


...Orthogonal Collocation
Application (heat)
Symmetric Polynomials
Legendre Polynomials
...Finite Element Method
...Calculus of Variations
...Splines
...Orth.Coll.Finite.Elem.
Hermite Polynomials
...Initial Value Techniques
Multiple conditions
Turn problem inside out
May work in only one direction
Sensitivity
...Method of Weighted Residuals
Application (heat)
...Errors
Richardson Extrapolation
...Comparison
...Adaptive Meshes
...Convective-Diffusion Eq.
...Singular Problems
...Infinite Domains
...Eigenvalue Problems


Partial Diff. Eq. (PDE-1D) ...Introduction
...Classification
...Separation of Variables
...Combination of Variables
...Numerical
...Finite Difference with MATLAB
...Spectral Methods
...Hyperbolic Equations
...Elliptic Equations
...Method of Weighted Residuals
...Finite Difference (Method of Lines)
...Orthogonal Collocation
...Finite Element Method
...Orth.Coll.Finite.Elem.
...Fast Fourier Transform
...Errors
...Stability
...Comparison


Elliptic Diff. Eq.
...Introduction
...Finite Difference
Direct
Iterative
...Orthogonal Collocation
...Finite Element Method
Adaptive Msh
Conjugate Gradient
Spines
...Comparison
...Navier-Stokes


Partial Diff. Eq. (PDE-2D)


Partial Diff. Eq. (Hyperbolic)
...Hyperbolic Eq.
...Convective-Diffusion Eq.
Steady
Advection
Convective Diffusion
...Finite Difference Method
Upwind
Fourier transform
MacCormack method
Flux Correction
Euler-Lagrange, sliding element
Random Choice
...Finite Element Method
Petrov-Galerkin
Flux-Correction


Integral Equations
...Classification
...Volterra, 2nd
...Fredholm, 2nd
...Eigenvalues
...Green's Function
...Boundary Integral


Probability & Statistics
...Concepts
...Sampling & Statistical
Decisions
...Error Analysis
...Factorial Design of Exp.
& Analysis of Variance


Parameter Estimation
...Linear Least Squares
...LS using MATLAB
...LS using EXCEL
...Curvefits with MATLAB


Fluid Flow
...Constitutive Equations
...Flow in Ducts (two fluids
...Finite Difference Method
...FD code
...Orthogonal Collocation Method
...OC code
...Flow of Polymers
...Finite Difference Method
...FD code
...Orthogonal Collocation Method
...OC code
...Flow in Ducts, Turbulent
...Boundary Layer Flows
...BL with IVP
...BL code
...BL with MWR
...Tank Drainage
...Derivation
...Tank Code
...2D flows past spheres
...2D entrance and exit flows
...Porous Media


Heat Transfer
...Constitutive Equations
...Heat Conduction (1D & 2D)
...Heat Transfer Coefficient
...Flow in Ducts, Rectilinear
...Fow in Ducts, Turbulent
...Boundary Layer Flows
...Compressible Flow
...PDEs in 1D
...Flow past spheres and cylinders
...Cross Flow Heat Exchangers


Mass Transfer
...Constitutive Equations
...PDEs in 1D
...Multiphase Diffusion
...Boundary Layer Flows
...Packed Beds (2 point BVP)
...Unsteady, Packed Beds


Chemical Reaction
...Diffusion and Reaction
...Diff.-Rxn.-Orth.Coll.
...Diff.-Rxn.-FD
..Orthogonal Collocation Code
...Finite Difference Code
...Initial Value Method
...Initial Value Code
...Flow Reactors
...Nonisothermal Problem
...Flow Reactors with Axial Dispersion
...Axial by Orthogonal Collocation
...Axial by Finite Difference
...Axial by Initial Value Methods
...Axial by OCFE
...Orthogonal Collocation Code
...Finite Difference Code
...Initial Value Code1
...Initial Value Code2
...OCFE Code
...Flow Reactors with Radial Dispersion
...Formulation of Equations
...Radial by Orthogonal Collocation
...Radial by Finite Difference
...Orthogonal Collocation Code
...Finite Difference Code


Thermodynamics
...pvt with cubic equation of state