Multirate generalized additive Runge Kutta methods
نویسندگان
چکیده
منابع مشابه
Multirate generalized additive Runge Kutta methods
This work constructs a new class of multirate schemes based on the recently developed generalized additive Runge-Kutta (GARK) methods [10]. Multirate schemes use different step sizes for different components and for different partitions of the right-hand side based on the local activity levels. We show that the new multirate GARK family includes many well-known multirate schemes as special case...
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This work generalizes the additively partitioned Runge-Kutta methods by allowing for different stage values as arguments of different components of the right hand side. An order conditions theory is developed for the new family of generalized additive methods, and stability and monotonicity investigations are carried out. The paper discusses the construction and properties of implicit-explicit ...
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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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Certain pairs of Runge-Kutta methods may be used additively to solve a system of n differential equations x' = J(t)x + g(t, x). Pairs of methods, of order p < 4, where one method is semiexplicit and /(-stable and the other method is explicit, are obtained. These methods require the LU factorization of one n X n matrix, and p evaluations of g, in each step. It is shown that such methods have a s...
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We propose some new additive Runge–Kutta methods of orders ranging from 2 to 4 that may be used for solving some nonlinear system of ODEs, especially for the temporal discretization of some nonlinear systems of PDEs with constraints. Only linear ODEs or PDEs need to be solved at each time step with these new methods. © 2005 Elsevier B.V. All rights reserved.
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ژورنال
عنوان ژورنال: Numerische Mathematik
سال: 2015
ISSN: 0029-599X,0945-3245
DOI: 10.1007/s00211-015-0756-z