NDLI: Internal Error Propagation in Explicit Runge--Kutta Methods

Content Provider	Society for Industrial and Applied Mathematics (SIAM)
Author	Ketcheson, David I. Lóczi, Lajos Parsani, Matteo
Copyright Year	2014
Abstract	In practical computation with Runge--Kutta methods, the stage equations are not satisfied exactly, due to roundoff errors, algebraic solver errors, and so forth. We show by example that propagation of such errors within a single step can have catastrophic effects for otherwise practical and well-known methods. We perform a general analysis of internal error propagation, emphasizing that it depends significantly on how the method is implemented. We show that for a fixed method, essentially any set of internal stability polynomials can be obtained by modifying the implementation details. We provide bounds on the internal error amplification constants for some classes of methods with many stages, including strong stability preserving methods and extrapolation methods. These results are used to prove error bounds in the presence of roundoff or other internal errors.
Starting Page	2227
Ending Page	2249
Page Count	23
File Format	PDF
ISSN	00361429
DOI	10.1137/130936245
e-ISSN	10957170
Issue Number	5
Volume Number	52
Language	English
Publisher	Society for Industrial and Applied Mathematics
Publisher Date	2014-09-11
Access Restriction	Subscribed
Subject Keyword	roundoff error ordinary differential equations extrapolation Multistep, Runge-Kutta and extrapolation methods Roundoff error strong stability preservation internal stability Error bounds Initial value problems Runge--Kutta methods
Content Type	Text
Resource Type	Article
Subject	Applied Mathematics Numerical Analysis Computational Mathematics

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