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Numerical solution of ordinary differential equations /

"This new work is an introduction to the numerical solution of the initial value problem for a system of ordinary differential equations. The first three chapters are general in nature, and chapters 4 through 8 derive the basic numerical methods, prove their convergence, study their stability a...

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Bibliographic Details
Main Author: Shampine, Lawrence F.
Corporate Author: Taylor & Francis
Format: eBook
Language:English
Published: New York : Chapman and Hall, 1994.
Series:Chapman & Hall mathematics.
Subjects:
Differential equations > Numerical solutions.
Équations différentielles > Solutions numériques.
Electronic books.
Online Access:Connect to the full text of this electronic book
Table of Contents:
  • Ch. 1. The Mathematical Problem
  • 1. Existence, Uniqueness and Standard Form
  • 2. Order
  • 3. Difficulties and Techniques for Handling Them
  • Ch. 2. Discrete Variable Methods
  • 1. Local Error
  • 2. Backward Error Analysis
  • 3. Stability
  • 4. Examples
  • Ch. 3. The Computational Problem
  • 1. Specifying the Differential Equation
  • 2. Output of the Solution
  • 3. Accuracy
  • 4. Storage Management and User Interface
  • 5. Software
  • Ch. 4. Basic Methods
  • 1. One-Step Methods
  • 2. Methods with Memory
  • 3. Implicit Methods
  • 4. General Remarks About Order
  • Ch. 5. Convergence and Stability
  • 1. One-Step Methods
  • 2. Some Methods with Memory
  • 3. Starting Methods with Memory
  • 4. Convergence with Constant Step Size
  • 5. Interpolation
  • 6. Computational Errors
  • 7. Variation of Order
  • 8. Problems That Are Not Smooth
  • Ch. 6. Stability for Large Step Sizes
  • 1. Stability with Respect to Small Perturbations
  • 2. A Special Class of Problems
  • 3. How Instability Is Manifested
  • 4. Constant Coefficient Difference Equations
  • Ch. 7. Error Estimation and Control
  • 1. Asymptotic Behavior of the Error
  • 2. Estimation of the Global, or True, Error
  • 3. Error Control, Step Size Adjustment, and Efficiency
  • 4. Asymptotic Analysis of Step Size Selection
  • 5. Error Estimators
  • 6. Starting a Code
  • Ch. 8. Stiff Problems
  • 1. What Is Stiffness?
  • 2. Methods Suitable for Stiff Problems
  • 3. Examples
  • Appendix: Some Mathematical Tools.