rdf-syntax-grammar
mods:
  schema location: http://www.loc.gov/mods/v3 http://www.loc.gov/standards/mods/v3/mods-3-2.xsd
  title info:
    title: Numerical solution of ordinary differential equations
  name:
    name part: Shampine, Lawrence F.
    role:
      role term: creator
  name:
    name part: Taylor & Francis
  type of resource: text
  genre: bibliography
  genre: Electronic books.
  origin info:
    place:
      place term: nyu
    place:
      place term: New York
    publisher: Chapman and Hall
    date issued: 1994
    issuance: monographic
  language:
    language term: eng
  physical description:
    form: remote
    extent: 1 online resource (x, 484 pages : illustrations.).
  abstract: "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.
  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.
  note: Lawrence F. Shampine.
  note: Includes bibliographical references (pages 452-460) and index.
  subject:
    topic: Differential equations
    topic: Numerical solutions
  subject:
    topic: Équations différentielles
    topic: Solutions numériques
  subject:
    topic: Differential equations
    topic: Numerical solutions
  classification: QA372 .S417 1994
  classification: 515/.352
  classification: 31.44
  classification: *65L05
  classification: 31.76
  classification: 34A34
  classification: 34E13
  classification: 65-02
  classification: 65L06
  classification: 65L20
  classification: 65L70
  classification: 519.62
  related item:
    identifier: (DLC) 93030156
  related item:
    title info:
      title: Chapman & Hall mathematics
  identifier: 9780203745328 (electronic bk)
  identifier: 0203745329 (electronic bk)
  identifier: 0412051516
  identifier: 9780412051517
  identifier: 9781351427555
  identifier: 1351427555
  identifier: 9781351427548
  identifier: 1351427547
  identifier: 93030156
  identifier: http://proxy.library.tamu.edu/login
  record info:
    record content source: AU@
    record creation date: 190323
    record change date: 20250728184616.1
    record identifier: in00005652676
    language of cataloging:
      language term: eng