Runge-Kutta Methods with Minimum Error Bounds
نویسندگان
چکیده
منابع مشابه
Runge-Kutta methods with minimum storage implementations
Solution of partial differential equations by the method of lines requires the integration of large numbers of ordinary differential equations (ODEs). In such computations, storage requirements are typically one of the main considerations, especially if a high order ODE solver is required. We investigate Runge-Kutta methods that require only two storage locations per ODE. Existing methods of th...
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Users of locally-adaptive software for initial value ordinary differential equations are likely to be concerned with global errors. At the cost of extra computation, global error estimation is possible. Zadunaisky's method and 'solving for the error estimate' are two techniques that have been successfully incorporated into Runge-Kutta algorithms. The standard error analysis for these techniques...
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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: 1962
ISSN: 0025-5718
DOI: 10.2307/2003133