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RungeKutta methods and renormalization
, 1999
"... A connection between the algebra of rooted trees used in renormalization theory and RungeKutta methods is pointed out. Butcher’s group and Bseries are shown to provide a suitable framework for renormalizing a toy model of field theory, following Kreimer’s approach. Finally Bseries are used to sol ..."
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Cited by 50 (0 self)
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A connection between the algebra of rooted trees used in renormalization theory and RungeKutta methods is pointed out. Butcher’s group and Bseries are shown to provide a suitable framework for renormalizing a toy model of field theory, following Kreimer’s approach. Finally Bseries are used
DIFFERENTIALALGEBRAIC EQUATIONS BY LOBATTO RUNGEKUTTA METHODS ∗
"... We consider the numerical solution of systems of index 2 implicit differentialalgebraic equations (DAEs) by a class of super partitioned additive Runge–Kutta (SPARK) methods. The families of Lobatto IIIABCC ∗D methods are included. We show superconvergence of optimal order 2s − 2forthesstage ..."
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We consider the numerical solution of systems of index 2 implicit differentialalgebraic equations (DAEs) by a class of super partitioned additive Runge–Kutta (SPARK) methods. The families of Lobatto IIIABCC ∗D methods are included. We show superconvergence of optimal order 2s − 2forthes
Date RUNGEKUTTA TYPE METHODS FOR DIFFERENTIALALGEBRAIC
, 2011
"... Differentialalgebraic equations (DAEs) consist of mixed systems of ordinary differential equations (ODEs) coupled with linear or nonlinear equations. Such systems may be viewed as ODEs with integral curves lying in a manifold. DAEs appear frequently in applications such as classical mechanics and e ..."
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and electrical circuits. This thesis concentrates on systems of index 2, originally index 3, and mixed index 2 and 3. Fast and efficient numerical solvers for DAEs are highly desirable for finding solutions. We focus primarily on the class of GaussLobatto SPARK methods. However, we also introduce an extension
Pseudosymplectic RungeKutta Methods
, 1997
"... . Apart from specific methods amenable to specific problems, symplectic RungeKutta methods are necessarily implicit. The aim of this paper is to construct explicit RungeKutta methods which mimic symplectic ones as far as the linear growth of the global error is concerned. Such method of order p h ..."
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Cited by 11 (1 self)
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test problems. AMS subject classification: 65L05. Key words: Hamiltonian systems, symplectic RungeKutta methods, pseudosymplectic RungeKutta methods, pseudosymplecticness conditions, simplifying assumptions. 1 Introduction. Let (H) be an autonomous Hamiltonian system (H) ( p 0 = \Gamma @H
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
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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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
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
Efficient rungekutta integrators for index2 differential algebraic equations
 Mathmatics of Computation
, 1998
"... Abstract. In seeking suitable RungeKutta methods for differential algebraic equations, we consider singlyimplicit methods to which are appended diagonallyimplicit stages. Methods of this type are either similar to those of Butcher and Cash or else allow for the importation of a final derivative f ..."
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Cited by 1 (0 self)
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Abstract. In seeking suitable RungeKutta methods for differential algebraic equations, we consider singlyimplicit methods to which are appended diagonallyimplicit stages. Methods of this type are either similar to those of Butcher and Cash or else allow for the importation of a final derivative
Another Approach to RungeKutta Methods
"... The condition equations are derived by the introduction of a system of equivalent differential equations, avoiding the usual formalism with trees and elementary differentials. Solutions to the condition equations are found by direct numerical optimization, during which simplifying assumptions upon t ..."
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the RungeKutta coefficients may or may not be used. Depending on the optimization criterion, different types of optimal RungeKutta methods can be pursued. In the present article the emphasis is on rounding minimization. Key words: RungeKutta, condition equations, direct optimization, rounding errors AMS
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