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Chapter 1. Introduction, pages 1-71
1-1 Classification of Equations
Chapter 2. Algebraic Equations, pages 8-16
2-1 Successive Substitution
2-2 Newton-Raphson
2-3 Comparison
Study Questions, Problems, and Bibliography
Chapter 3. Ordinary Differential Equations-Initial-Value Problems, pages 17-59
3-1 Terminology
3-2 Interpolation and Quadrature
3-3 Explicit Integration Methods
3-4 Implicit Integration Methods
3-5 Predictor-Corrector and Runge-Kutta Method
3-6 Extrapolation and Step-Size Control
3-7 Stability
3-8 High-order Schemes that are Stable and do not Oscillate
3-9 Equation Solvers
3-10 Comparison
Study Questions, Problems, Bibliography, References
Chapter 4. Ordinary Differential Equations-Boundary-Value Problems, pages 60-171
4-1 Method of Weighted Residuals
4-2 Finite Difference Method
4-3 Regular Perturbation
4-4 Orthogonal Collocation
4-5 Diffusion and Reaction-Exact Results
4-6 Perturbation Method for Diffusion and Reaction
4-7 Orthogonal Collocation for Diffusion and Reaction
4-8 Lower-Upper Decomposition of Matrices
4-9 Orthogonal Collocation on Finite Elements
4-10 Galerkin Finite Elements
4-11 Initial-Value Techniques
4-12 Quasilinearization
4-13 Comparison
4-14 Adaptive Meshes
Study Questions, Problems, Bibliography, References
Chapter 5. Parabolic Partial Differential Equations-Time and
One Spatial Dimension, pages 172-272
5-1 Similarity Transformation
5-2 Separation of Variables
5-3 Method of Weighted Residuals
5-4 Orthogonal Collocation
5-5 Finite Difference
5-6 Orthogonal Collocation on Finite Elements
5-7 Galerkin Finite Element Method
5-8 Convective Diffusion Equation
5-9 Flow Through Porous Media
5-10 Comparison
Study Questions, Problems, Bibliography, References
Chapter 6. Partial Differential Equations in Two Space Dimensions, pages 272-315
6-1 Introduction
6-2 Finite Difference
6-3 Orthogonal Collocation
6-4 Galerkin Finite Element Method
6-5 Comparison
Problems, Bibliography, References
Errata
Author Index
Subject Index