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The Dynamics of RungeKutta Methods
 Int. J. Bifurcation and Chaos
, 1992
"... this paper, we attempt to elucidate the dynamics of the most commonly used family of numerical integration schemes, RungeKutta methods, by the application of the techniques of dynamical systems theory to the maps produced in the numerical analysis. QMW preprint DYN #919, Int. J. Bifurcation and C ..."
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Cited by 32 (4 self)
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this paper, we attempt to elucidate the dynamics of the most commonly used family of numerical integration schemes, RungeKutta methods, by the application of the techniques of dynamical systems theory to the maps produced in the numerical analysis. QMW preprint DYN #919, Int. J. Bifurcation
Accelerated RungeKutta Methods
, 2008
"... Standard RungeKutta methods are explicit, onestep, and generally constant stepsize numerical integrators for the solution of initial value problems. Such integration schemes of orders 3, 4, and 5 require 3, 4, and 6 function evaluations per time step of integration, respectively. In this paper, w ..."
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Cited by 4 (0 self)
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, we propose a set of simple, explicit, and constant stepsize AccerelatedRungeKutta methods that are twostep in nature. For orders 3, 4, and 5, they require only 2, 3, and 5 function evaluations per time step, respectively. Therefore, they are more computationally efficient at achieving the same
Numerical Solutions of the Euler Equations by Finite Volume Methods Using RungeKutta TimeStepping Schemes
, 1981
"... A new combination of a finite volume discretization in conjunction with carefully designed dissipative terms of third order, and a Runge Kutta time stepping scheme, is shown to yield an effective method for solving the Euler equations in arbitrary geometric domains. The method has been used to deter ..."
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Cited by 456 (78 self)
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A new combination of a finite volume discretization in conjunction with carefully designed dissipative terms of third order, and a Runge Kutta time stepping scheme, is shown to yield an effective method for solving the Euler equations in arbitrary geometric domains. The method has been used
RungeKutta Research in Trondheim
"... RungeKutta research in Trondheim began in 1970 when Syvert P. Nørsett was appointed to the NTH. Although the group has worked on various aspects of RungeKutta methods, we have elected, in this paper, to focus on DIRK methods, linear stability, order stars, parallel methods and continuous explicit ..."
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Cited by 1 (0 self)
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RungeKutta research in Trondheim began in 1970 when Syvert P. Nørsett was appointed to the NTH. Although the group has worked on various aspects of RungeKutta methods, we have elected, in this paper, to focus on DIRK methods, linear stability, order stars, parallel methods and continuous explicit
Regular RungeKutta Pairs
 APPLIED NUMERICAL MATHEMATICS
, 1997
"... Timestepping methods that guarantee to avoid spurious fixed points are said to be regular. For fixed stepsize RungeKutta formulas, this concept has been well studied. Here, the theory of regularity is extended to the case of embedded RungeKutta pairs used in variable stepsize mode with local erro ..."
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Cited by 2 (1 self)
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Timestepping methods that guarantee to avoid spurious fixed points are said to be regular. For fixed stepsize RungeKutta formulas, this concept has been well studied. Here, the theory of regularity is extended to the case of embedded RungeKutta pairs used in variable stepsize mode with local
A family of fifthorder Runge–Kutta pairs
 Math. Comp
, 1996
"... Abstract. The construction of a RungeKutta pair of order 5(4) with the minimal number of stages requires the solution of a nonlinear system of 25 order conditions in 27 unknowns. We define a new family of pairs which includes pairs using 6 function evaluations per integration step as well as pairs ..."
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Cited by 2 (0 self)
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Abstract. The construction of a RungeKutta pair of order 5(4) with the minimal number of stages requires the solution of a nonlinear system of 25 order conditions in 27 unknowns. We define a new family of pairs which includes pairs using 6 function evaluations per integration step as well as pairs
Derivation of Efficient Continuous Explicit RungeKutta Methods
 SIAM J. Sci. Stat. Comput
, 1992
"... . Continuous Explicit RungeKutta methods with the minimal number of stages are considered. These methods are continuously differentiable if and only if one of the stages is the FSAL evaluation. A characterization of a subclass of these methods is developed for order 3,4 and 5. It is shown how the f ..."
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Cited by 13 (1 self)
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. Continuous Explicit RungeKutta methods with the minimal number of stages are considered. These methods are continuously differentiable if and only if one of the stages is the FSAL evaluation. A characterization of a subclass of these methods is developed for order 3,4 and 5. It is shown how
A Survey of the Explicit RungeKutta Method
, 1995
"... Research in explicit RungeKutta methods is producing continual improvements to the original algorithms, and the aim of this survey is to relate the current stateoftheart. In drawing attention to recent advances, we hope to provide useful information for those who apply numerical methods. We desc ..."
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Cited by 16 (2 self)
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describe recent work in the derivation of RungeKutta coefficients: "classical" generalpurpose formulas, "special" formulas for high order and Hamiltonian problems, and "continuous" formulas for dense output. We also give a thorough review of implementation details. Modern
Classical Fourth Order RungeKutta..................................................................
, 2010
"... 10 RungeKuttaGill................................................................................................ 10 Fehlberg RKF45................................................................................................. 10 Adams PredictorCorrector......................................... ..."
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10 RungeKuttaGill................................................................................................ 10 Fehlberg RKF45................................................................................................. 10 Adams Predictor
Results 1  10
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