Numerical solution of ordinary differential equations. (2018)

• Record Type: Book
• Further Information: Note: Lawrence F. Shampine.
• Other Names: Shampine, Lawrence F
• 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.
• Publisher Details: Place of publication not identified : Routledge
• Publication Date: 2018
• Extent: 1 online resource (632 pages)
• Subjects: 515/.352; Differential equations -- Numerical solutions; Differential equations -- Numerical solutions; Gewone differentiaalvergelijkingen; Oplossingen (wiskunde); Équations différentielles -- Solutions numériques
• Languages: English
• ISBNs: 9781351427548; 1351427547
• Access Rights: Legal Deposit; Only available on premises controlled by the deposit library and to one user at any one time; The Legal Deposit Libraries (Non-Print Works) Regulations (UK).
• Access Usage: Restricted: Printing from this resource is governed by The Legal Deposit Libraries (Non-Print Works) Regulations (UK) and UK copyright law currently in force.