Runge–Kutta methods

Known as: Runge kutta, Butcher table, Runge Kutta Method 
In numerical analysis, the Runge–Kutta methods are a family of implicit and explicit iterative methods, which includes the well-known routine called… (More)
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ApproximationBackward Euler methodBulirsch–Stoer algorithmCash–Karp method
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Papers overview

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2010
2010
Optimum Runge-Kutta Methods
The optimum Runge-Kutta method of a particular order is the one whose truncation error is a minimum. Various measures of the size… (More)
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2010
2010
Natural Continuous Extensions of Runge-Kutta Methods
The present paper develops a theory of Natural Continuous Extensions (NCEs) for the discrete approximate solution of an ODE given… (More)
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2008
2008
ENERGY-PRESERVING RUNGE-KUTTA METHODS
We show that while Runge-Kutta methods cannot preserve polynomial invariants in general, they can preserve polynomials that are… (More)
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2007
2007
Runge-Kutta methods
Runge Kutta methods are used to solve ordinary differential equations. Ordinary Differential Equations have a wide application… (More)
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2006
2006
Efficient symplectic Runge-Kutta methods
The present paper continues the research in [H.Y. Liu, G. Sun, Symplectic RK methods and symplectic PRK methods with real… (More)
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Highly Cited
2003
Highly Cited
2003
Implicit-explicit Runge-Kutta methods for time-dependent partial differential equations
Implicit-explicit (IMEX) linear multistep time-discretization schemes for partial differential equations have proved useful in… (More)
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2000
2000
Exponentially tted Runge – Kutta methods (
Exponentially tted Runge–Kutta methods with s stages are constructed, which exactly integrate di erential initial-value problems… (More)
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Highly Cited
1999
Highly Cited
1999
High order Runge-Kutta methods on manifolds "
We present a family of Runge-Kutta type integration schemes of arbitrarily high order for differential equations evolving on… (More)
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1999
1999
Runge-Kutta methods and renormalization
  • Ch. Brouder
  • 1999
A connection between the algebra of rooted trees used in renormalization theory and Runge-Kutta methods is pointed out. Butcher’s… (More)
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1997
1997
Pseudo-symplectic Runge-kutta Methods
Apart from speciic methods amenable to speciic problems, symplectic Runge-Kutta methods are necessarily implicit. The aim of this… (More)
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