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Runge–Kutta methods
Known as:
Runge kutta
, Butcher table
, Runge Kutta Method
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In numerical analysis, the Runge–Kutta methods are a family of implicit and explicit iterative methods, which includes the well-known routine called…
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Related topics
Related topics
38 relations
Approximation
Backward Euler method
Bulirsch–Stoer algorithm
Cash–Karp method
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Papers overview
Semantic Scholar uses AI to extract papers important to this topic.
Highly Cited
2005
Highly Cited
2005
Explicit Exponential Runge-Kutta Methods for Semilinear Parabolic Problems
M. Hochbruck
,
A. Ostermann
SIAM Journal on Numerical Analysis
2005
Corpus ID: 14172832
The aim of this paper is to analyze explicit exponential Runge--Kutta methods for the time integration of semilinear parabolic…
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Highly Cited
2005
Highly Cited
2005
Runge-Kutta Discontinuous Galerkin Method Using WENO Limiters
J. Qiu
,
Chi-Wang Shu
SIAM Journal on Scientific Computing
2005
Corpus ID: 34758865
The Runge--Kutta discontinuous Galerkin (RKDG) method is a high order finite element method for solving hyperbolic conservation…
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Review
2001
Review
2001
Runge–Kutta Discontinuous Galerkin Methods for Convection-Dominated Problems
Bernardo Cockburn
,
Chi-Wang Shu
Journal of Scientific Computing
2001
Corpus ID: 14413497
In this paper, we review the development of the Runge–Kutta discontinuous Galerkin (RKDG) methods for non-linear convection…
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Highly Cited
2000
Highly Cited
2000
Runge-Kutta methods in optimal control and the transformed adjoint system
W. Hager
Numerische Mathematik
2000
Corpus ID: 16715381
Summary. The convergence rate is determined for Runge-Kutta discretizations of nonlinear control problems. The analysis utilizes…
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Highly Cited
1998
Highly Cited
1998
Total variation diminishing Runge-Kutta schemes
S. Gottlieb
,
Chi-Wang Shu
Mathematics of Computation
1998
Corpus ID: 2831572
In this paper we further explore a class of high order TVD (total variation diminishing) Runge-Kutta time discretization…
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Highly Cited
1994
Highly Cited
1994
Fourth-order 2N-storage Runge-Kutta schemes
M. Carpenter
,
C. Kennedy
1994
Corpus ID: 116658826
A family of five-stage fourth-order Runge-Kutta schemes is derived; these schemes required only two storage locations. A…
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Highly Cited
1994
Highly Cited
1994
Low-Dissipation and Low-Dispersion Runge-Kutta Schemes for Computational Acoustics
F. Hu
,
M. Y. Hussaini
,
J. Manthey
1994
Corpus ID: 16473786
In this paper, we investigate accurate and efficient time advancing methods for computational acoustics, where nondissipative and…
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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
J. Cash
,
A. Karp
TOMS
1990
Corpus ID: 1133671
Explicit Runge-Kutta methods (RKMs) are among the most popular classes of formulas for the approximate numerical integration of…
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Highly Cited
1989
Highly Cited
1989
The numerical solution of differential-algebraic systems by Runge-Kutta methods
E. Hairer
,
C. Lubich
,
M. Roche
1989
Corpus ID: 60632740
The term differential-algebraic equation was coined to comprise differential equations with constraints (differential equations…
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Highly Cited
1977
Highly Cited
1977
Diagonally implicit runge-kutta methods for stiff odes
R. Alexander
1977
Corpus ID: 121638240
To be A-stable, and possibly useful for stiff systems, a Runge–Kutta formula must be implicit. There is a significant…
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