Results 121 to 130 of about 10,395 (165)
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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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Efficient symplectic Runge–Kutta methods
Applied Mathematics and Computation, 2006The authors consider the efficiency of symplectic Runge-Kutta methods with real eigenvalues for the numerical integration of initial value problems for systems of ordinary differential equations.
Chan, R. P. K., Liu, Hongyu, Sun, Geng
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Runge-Kutta methods: some historical notes
Applied Numerical Mathematics, 1996We cite from the abstract: ``\(\ldots\) This centenary history of Runge-Kutta methods contains an appreciation of the early work of Runge, Heun, Kutta, and Nyström and a survey of some significant developments of these methods over the last hundred years.
Butcher, J.C., Wanner, Gerhard
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Interpolation for Runge–Kutta Methods
SIAM Journal on Numerical Analysis, 1985The author discusses a new method for interpolation between mesh points of Runge-Kutta algorithms for the approximate solution of ordinary differential equations. The method is shown to fall under the classification of scaled Runge-Kutta algorithms as considered by \textit{M. K. Horn} [ibid. 20, 558-568 (1983; Zbl 0511.65048)].
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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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Embedded Pseudo-Runge–Kutta Methods
SIAM Journal on Numerical Analysis, 1991This paper deals with embedded pseudo-Runge-Kutta methods and their use in step size control without additional function evaluations. There is a report on results of a number of numerical experiments.
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Extrapolated stabilized explicit Runge–Kutta methods
Journal of Computational Physics, 2016zbMATH Open Web Interface contents unavailable due to conflicting licenses.
J. Martín-Vaquero, B. Kleefeld
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Linearly-implicit Runge-Kutta methods based on implicit Runge-Kutta methods
Applied Numerical Mathematics, 1993Linearly-implicit Runge-Kutta methods (LIRKM), based on explicit Runge- Kutta schemes, are compared with implicit Runge-Kutta methods (IRKM) which require the solution of nonlinear equations by Newton-like methods. In particular, the consistency of LIRKM is investigated and the numerical expense of IRKM and LIRKM is considered.
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BIT, 1985
A Runge-Kutta method (for the numerical solution of ordinary differential equations) is called reducible if there exists a method with ...
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A Runge-Kutta method (for the numerical solution of ordinary differential equations) is called reducible if there exists a method with ...
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Positivity of Runge-Kutta and diagonally split Runge-Kutta methods
Applied Numerical Mathematics, 1998The author investigates positivity of general Runge-Kutta and diagonally split Runge-Kutta methods for the numerical solution of positive initial value problems for ordinary differential equations. Conditions for the maximal stepsize in term of the radius of positivity of the Runge-Kutta method which guarantees positivity are given.
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