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Computational mathematics in engineering and applied science : ODEs, DAEs, and PDEs
- Author / Creator
- Available as
- Physical
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- Creator
- William E. Schiesser
- Format
- Books
- Language
- English
- Publication
-
- Boca Raton, Fla. ; London : CRC Press, 1994
- Physical Details
-
- viii, 587 pages : illustrations ; 26 cm
- ISBNs
- 0849373735, 9780849373732
- OCLC
- ocm30977022
- Includes index.
- 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