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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… Expand
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Related topics

Related topics

38 relations
ApproximationBackward Euler methodBulirsch–Stoer algorithmCash–Karp method
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Papers overview

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Highly Cited
2005
Highly Cited
2005
Explicit Exponential Runge-Kutta Methods for Semilinear Parabolic Problems
The aim of this paper is to analyze explicit exponential Runge--Kutta methods for the time integration of semilinear parabolic… Expand
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Highly Cited
1998
Highly Cited
1998
Total variation diminishing Runge-Kutta schemes
In this paper we further explore a class of high order TVD (total variation diminishing) Runge-Kutta time discretization… Expand
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Highly Cited
1997
Highly Cited
1997
Implicit-explicit Runge-Kutta methods for time-dependent partial differential equations
Abstract Implicit-explicit (IMEX) linear multistep time-discretization schemes for partial differential equations have proved… Expand
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Highly Cited
1994
Highly Cited
1994
Low-Dissipation and Low-Dispersion Runge-Kutta Schemes for Computational Acoustics
In this paper, we investigate accurate and efficient time advancing methods for computational acoustics, where nondissipative and… Expand
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Highly Cited
1994
Highly Cited
1994
Fourth-order 2N-storage Runge-Kutta schemes
A family of five-stage fourth-order Runge-Kutta schemes is derived; these schemes require only two storage locations. A… Expand
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Highly Cited
1990
Highly Cited
1990
A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides
Explicit Runge-Kutta methods (RKMs) are among the most popular classes of formulas for the approximate numerical integration of… Expand
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Highly Cited
1990
Highly Cited
1990
The Runge-Kutta local projection discontinuous Galerkin finite element method for conservation laws. IV. The multidimensional case
In this paper we study the two-dimensional version of the Runge- Kutta Local Projection Discontinuous Galerkin (RKDG) methods… Expand
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Highly Cited
1989
Highly Cited
1989
TVB Runge-Kutta local projection discontinuous Galerkin finite element method for conservation laws. II. General framework
Construction et analyse d'une classe de methodes a elements finis de Galerkin discontinues a variation totale bornee pour la… Expand
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Highly Cited
1989
Highly Cited
1989
The Numerical Solution Of Differential-Algebraic Systems By Runge-Kutta Methods
The term differential-algebraic equation was coined to comprise differential equations with constraints (differential equations… Expand
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Highly Cited
1977
Highly Cited
1977
Diagonally implicit runge-kutta methods for stiff odes
To be A-stable, and possibly useful for stiff systems, a Runge–Kutta formula must be implicit. There is a significant… Expand
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