Comparing Error Estimators for Runge-Kutta Methods
نویسندگان
چکیده
منابع مشابه
On the Construction of Error Estimators for Implicit Runge{Kutta Methods
For implicit Runge{Kutta methods intended for stii ODEs or DAEs, it is often diicult to embed a local error estimating method which gives realistic error estimates for stii/algebraic components. If the embedded method's stability function is unbounded at z = 1, stii error components are grossly overestimated. In practice some codes \improve" such inadequate error estimates by premultiplying the...
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Abstract— General linear methods (GLM) apply to a large family of numerical methods for ordinary differential equations, with RungeKutta (RK) and Almost Runge-Kutta (ARK) methods as two out of a number of special cases. In this paper, we have investigated the efficacy of Richardson extrapolation (RE) technique as a means of obtaining viable and acceptable estimates of the local truncation error...
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Literature For a great deal of information on Runge-Kutta methods consult J.C. Butcher, Numerical Methods for Ordinary Differential Equations, second edition, Wiley and Sons, 2008, ISBN 9780470723357. That book also has a good introduction to linear multistep methods. In these notes we refer to this books simply as Butcher. The notes were written independently of the book which accounts for som...
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ژورنال
عنوان ژورنال: Mathematics of Computation
سال: 1971
ISSN: 0025-5718
DOI: 10.2307/2005206