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Computational mathematics in engineering and applied science : ODEs, DAEs, and PDEs /

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Bibliographic Details
Main Author: Schiesser, W. E.
Corporate Author: Taylor & Francis
Format: eBook
Language:English
Published: Boca Raton, FL : CRC Press, 1993.
Subjects:
Engineering mathematics.
Differential equations.
Mathematical models.
Models, Theoretical
Mathématiques de l'ingénieur.
Équations différentielles.
Modèles mathématiques.
mathematical models.
Electronic books.
Online Access:Connect to the full text of this electronic book
Table of Contents:
  • 1. The General Problems in Ordinary, Differential Algebraic and Partial Differential Equations. 1.1. The ODE Problem. 1.2. The PDE Problem
  • 2. The Numerical Integration of Initial Value Ordinary Differential Equations. 2.1. An Example of What Can Go Wrong. 2.2. The Solution-Use a Quality ODE Integrator. 2.3. Single-Step Methods. 2.4. Multistep Methods. 2.5. Some Unconventional Uses of ODE Integrators
  • 3. Partial Differential Equations First Order in Time. 3.1. PDEs with Zeroth-Order and First-Order Spatial Derivatives. 3.2. PDEs with Second-Order Spatial Derivatives
  • 4. Partial Differential Equations First Order in Time (continued). 4.1. PDEs with First- and Second-Order Spatial Derivatives. 4.2. Nonuniform Spatial Grids. 4.3. PDEs with Mixed Partial Derivatives.
  • 4.4. PDE Solution with a DAE Solver. 4.5. Multiregion PDEs. 4.6. Bandwidth Reduction in the Method of Lines. 4.7. Weighted Residual Methods. 4.8. The Finite Element Method. 4.9. The Finite Volume Method. 4.10. A Two-Dimensional Advective Equation
  • 5. Partial Differential Equations Second and Zeroth Order in Time. 5.1. PDEs Second Order in Time. 5.2. PDEs Zeroth Order in Time. 5.3. Conclusions
  • A: A Second-Order Adams-Bashforth ODE Integrator
  • B: Spatial Differentiation Routines
  • C: Library of ODE/DAE/PDE Applications.