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Perturbed Runge–Kutta Methods for Mixed Precision Applications
Journal of Scientific Computing, 2020In this work we consider a mixed precision approach to accelerate the implementation of multi-stage methods. We show that Runge–Kutta methods can be designed so that certain costly intermediate computations can be performed as a lower-precision ...
Zachary J. Grant
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Diagonally implicit Runge–Kutta methods for stiff ODEs
, 2019Based principally on a recent review of diagonally implicit Runge–Kutta (DIRK) methods applied to stiff first-order ordinary differential equations (ODEs) by the present authors, several nearly optimal, general purpose, DIRK-type methods are presented ...
C. Kennedy, M. Carpenter
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Stabilitätseigenschaften adaptiver Runge -Kutta-Verfahren
ZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik, 1981AbstractZur numerischen Behandlung von steifen Anfangswertaufgaben wird eine Klasse adaptiver Runge‐Kutta‐Verfahren betrachtet. Unter Beibehaltung der Konsistenzordnung erfordern sie nur gelegentlich eine Berechnung der Jacobi‐Matrix. Das Stabilitätsverhalten der adaptiven Verfahren bei großen Schrittweiten wird bezüglich des von Prothero und Robinson ...
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2019
The class of differential equations for which explicit solutions can be obtained is rather small. In fact, in Chap. 3, we have already remarked that to find an explicit solution of the second-order linear differential equation ( 3.2) there does not exist any method.
Ravi P. Agarwal +2 more
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The class of differential equations for which explicit solutions can be obtained is rather small. In fact, in Chap. 3, we have already remarked that to find an explicit solution of the second-order linear differential equation ( 3.2) there does not exist any method.
Ravi P. Agarwal +2 more
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Improved Runge–Kutta–Chebyshev methods
Mathematics and Computers in Simulation, 2020zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Tang, Xiao, Xiao, Aiguo
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Convolutional neural networks combined with Runge–Kutta methods
Neural computing & applications (Print), 2018A convolutional neural network can be constructed using numerical methods for solving dynamical systems, since the forward pass of the network can be regarded as a trajectory of a dynamical system.
Mai Zhu, B. Chang, Chong Fu
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Multirate Partitioned Runge-Kutta Methods
BIT Numerical Mathematics, 2001zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Günther, M., Kværnø, A., Rentrop, P.
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Runge–Kutta methods in elastoplasticity
Applied Numerical Mathematics, 2002zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Büttner, Jörg, Simeon, Bernd
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1973
One-step methods (see Def. 2.1.8) form a particularly simple class of f. s. m. for IVP 1. Among these, a certain class of methods has commonly been associated with the names of C. Runge and W. Kutta and is widely used. These “Runge-Kutta methods” (RK-methods) are 1-step m+1-stage methods in the sense of Def. 2.1.10.
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One-step methods (see Def. 2.1.8) form a particularly simple class of f. s. m. for IVP 1. Among these, a certain class of methods has commonly been associated with the names of C. Runge and W. Kutta and is widely used. These “Runge-Kutta methods” (RK-methods) are 1-step m+1-stage methods in the sense of Def. 2.1.10.
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Extended Runge–Kutta-like formulae
Applied Numerical Mathematics, 2006zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Wu, Xinyuan, Xia, Jianlin
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