Scienlific Computing and Differential Equations

Title page
Preface
Chapter 1. The World of Scientific Computing
1.1 What is Scientific Computing?
1.2 Mathematical Modeling
1.3 The Process of Numerical Solution
1.4 The Computational Environment
Chapter 2. Letting It Fly: Initial Value Problems
2.1 Examples of Initial Value Problems
2.2 One-Step Methods
2.3 Polynomial Interpolation
2.4 Multistep Methods
2.5 Stability, Instability, and Stiff Equations
Chapter 3. Pinning It Down: Boundary Value Problems
3.1 The Finite Difference Method for Linear Problems
3.2 Solution of the Discretized Problem
Chapter 4. More on Linear Systems of Equations
4.1 Introduction and Least Squares Problems
4.2 Gaussian Elimination
4.3 Interchanges
4.4 Ill-conditioning and Error Analysis
4.5 Other Factorizations
Chapter 5. Life Is Really Nonlinear
5.1 Nonlinear Problems and Shooting
5.2 Solution of a Single Nonlinear Equation
5.3 Systems of Nonlinear Equations
Chapter 6. Is There More Than Finite Differences?
6.1 Introduction to Projection Methods
6.2 Spline Approximation
6.3 Numerical Integration
6.4 The Discrete Problem Using Splines
Chapter 7. N Important Numbers
7.1 Eigenvalue Problems
7.2 The QR Method
7.3 Other Iterative Methods
Chapter 8. Space and Time
8.1 Partial DifferentiaI Equations
8.2 Explicit Methods and Stability
8.3 Implicit Methods
8.4 Semidiscrete Methods
Chapter 9. The Curse of Dimensionality
9.1 Two and Three Space Dimensions
9.2 Direct Methods
9.3 Iterative Methods
Appendix 1. Analysis and Differential Equations
Appendix 2. Linear Aigebra
Bibliography
Author Index
Subject Index