Analysis of Discretization Methods for Ordinary Differential Equations
Due to the fundamental role of differential equations in science and engineering it has long been a basic task of numerical analysts to generate numerical values of solutions to differential equations. Nearly all approaches to this task involve a "finitization" of the original differential...
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| Format: | eBook |
| Language: | English |
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Berlin, Heidelberg
Springer Berlin Heidelberg
1973, 1973
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| Edition: | 1st ed. 1973 |
| Series: | Springer Tracts in Natural Philosophy
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| Subjects: | |
| Online Access: | |
| Collection: | Springer Book Archives -2004 - Collection details see MPG.ReNa |
Table of Contents:
- 1 General Discretization Methods
- 1.1. Basic Definitions
- 1.2 Results Concerning Stability
- 1.3 Asymptotic Expansions of the Discretization Errors
- 1.4 Applications of Asymptotic Expansions
- 1.5 Error Analysis
- 1.6 Practical Aspects
- 2 Forward Step Methods
- 2.1 Preliminaries
- 2.2 The Meaning of Consistency, Convergence, and Stability with Forward Step Methods
- 2.3 Strong Stability of f.s.m.
- 3 Runge-Kutta Methods
- 3.1 RK-procedures
- 3.2 The Group of RK-schemes
- 3.3 RK-methods and Their Orders
- 3.4 Analysis of the Discretization Error
- 3.5 Strong Stability of RK-methods
- 4 Linear Multistep Methods
- 4.1 Linear k-step Schemes
- 4.2 Uniform Linear k-step Methods
- 4.3 Cyclic Linear k-step Methods
- 4.4 Asymptotic Expansions
- 4.5 Further Analysis of the Discretization Error
- 4.6 Strong Stability of Linear Multistep Methods
- 5 Multistage Multistep Methods
- 5.1 General Analysis
- 5.2 Predictor-corrector Methods
- 5.3 Predictor-corrector Methods with Off-step Points
- 5.4 Cyclic Forward Step Methods
- 5.5 Strong Stability
- 6 Other Discretization Methods for IVP 1
- 6.1 Discretization Methods with Derivatives of f
- 6.2 General Multi-value Methods
- 6.3 Extrapolation Methods