Author | Stetter, Hans J. author |
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Title | Analysis of Discretization Methods for Ordinary Differential Equations [electronic resource] / by Hans J. Stetter |
Imprint | Berlin, Heidelberg : Springer Berlin Heidelberg, 1973 |
Connect to | http://dx.doi.org/10.1007/978-3-642-65471-8 |
Descript | XVI, 390 p. online resource |
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