http://www.loc.gov/mods/v3 http://www.loc.gov/standards/mods/v3/mods-3-2.xsd
Numerical solution of ordinary differential equations
1 online resource (x, 484 pages : illustrations.).
"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 and consider how to implement them effectively. The book focuses on the most important methods in practice and develops them fully, uses examples throughout, and emphasizes practical problem-solving methods."--Amazon.
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.
Includes bibliographical references (pages 452-460) and index.