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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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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
PRECONDITIONING OF IMPLICIT RUNGEKUTTA METHODS
"... Abstract. A major problem in obtaining an efficient implementation of fully implicit RungeKutta (IRK) methods applied to systems of differential equations is to solve the underlying systems of nonlinear equations. Their solution is usually obtained by application of modified Newton iterations with ..."
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Abstract. A major problem in obtaining an efficient implementation of fully implicit RungeKutta (IRK) methods applied to systems of differential equations is to solve the underlying systems of nonlinear equations. Their solution is usually obtained by application of modified Newton iterations
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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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
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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. 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
Multistep RungeKutta Methods for solving DAEs
"... MULTISTEP RUNGEKUTTA METHODS FOR SOLVING DAEs. Several methods have been used by some authors to solve Differential Algebraic Equations (DAEs), the methods range from multistep methods such as BDF and EBDF methods to onestep methods such as RungeKutta methods. In this paper, we present Multistep ..."
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MULTISTEP RUNGEKUTTA METHODS FOR SOLVING DAEs. Several methods have been used by some authors to solve Differential Algebraic Equations (DAEs), the methods range from multistep methods such as BDF and EBDF methods to onestep methods such as RungeKutta methods. In this paper, we present Multistep
A RungeKutta BVODE Solver . . .
, 2013
"... Boundary value ordinary differential equations (BVODEs) are systems of ODEs with boundary conditions imposed at two or more distinctpoints. The global error(GE) of a numerical solution to a BVODE is the amount by which the numerical solution differs from the exact solution. Thedefect is the amount b ..."
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Boundary value ordinary differential equations (BVODEs) are systems of ODEs with boundary conditions imposed at two or more distinctpoints. The global error(GE) of a numerical solution to a BVODE is the amount by which the numerical solution differs from the exact solution. Thedefect is the amount
Results 1  10
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424,074