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AN IMPLICIT RUNGEKUTTA METHOD FOR GENERAL SECOND ORDER ORDINARY DIFFERENTIAL EQUATIONS
"... Abstract. This paper focuses on the derivation of a fully implicit Sixth order Rungekutta type method with error estimation formula for the solution of general second order ordinary differential equations (ODEs). We define a transformation on the set of coefficients (Butcher coefficients Tableau) f ..."
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Abstract. This paper focuses on the derivation of a fully implicit Sixth order Rungekutta type method with error estimation formula for the solution of general second order ordinary differential equations (ODEs). We define a transformation on the set of coefficients (Butcher coefficients Tableau
Runge–Kutta methods for linear ordinary differential equations
 Appl. Numer. Math
, 1999
"... Three new RungeKutta methods are presented for numerical integration of systems of linear inhomogeneous ordinary differential equations (ODEs) with constant coefficients. Such ODEs arise in the numerical solution of the partial differential equations governing linear wave phenomena. The restriction ..."
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Cited by 4 (2 self)
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Three new RungeKutta methods are presented for numerical integration of systems of linear inhomogeneous ordinary differential equations (ODEs) with constant coefficients. Such ODEs arise in the numerical solution of the partial differential equations governing linear wave phenomena
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
Redacted for Privacy Globally Optimal RungeKutta Methods
, 1973
"... Abstract approved: (J. Davis) A RungeKutta method has been developed to minimize the global error in the numerical solution of certain classes of differential equations problems. The distinguishing feature of the method is that the coefficients of the numerical integration formula depend on the ini ..."
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Abstract approved: (J. Davis) A RungeKutta method has been developed to minimize the global error in the numerical solution of certain classes of differential equations problems. The distinguishing feature of the method is that the coefficients of the numerical integration formula depend
Symmetric Partitioned RungeKutta Methods for Differential Equations on Lie Groups I
"... In this paper, we develop a higher order symmetric partitioned RungeKutta method for a coupled system of differential equations on Lie groups. We start with a discussion on partitioned RungeKutta methods on Lie groups of arbitrary order. As symmetry is not met for higher orders, we generalize the ..."
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In this paper, we develop a higher order symmetric partitioned RungeKutta method for a coupled system of differential equations on Lie groups. We start with a discussion on partitioned RungeKutta methods on Lie groups of arbitrary order. As symmetry is not met for higher orders, we generalize
Improving the Efficiency of RungeKutta Methods for the Solution of BVPs for HigherOrder ODEs
, 1996
"... Improving the Efficiency of RungeKutta Methods for the Solution of BVPs for HigherOrder ODEs Khalid Zuberi Master of Science Graduate Department of Computer Science University of Toronto, 1996 RungeKutta methods are often used to solve twopoint boundary value problems (BVPs) for ordinary ..."
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Improving the Efficiency of RungeKutta Methods for the Solution of BVPs for HigherOrder ODEs Khalid Zuberi Master of Science Graduate Department of Computer Science University of Toronto, 1996 RungeKutta methods are often used to solve twopoint boundary value problems (BVPs) for ordinary
EXPLICIT TWOSTEP RUNGEKUTTA METHODS
, 1994
"... Summary. The explicit twostep RungeKutta (TSRK) formulas for the numerical so lution of ordinary differential equations are analyzed. The order conditions are derived and the construction of such methods based on some simplifying assumptions is described. Order barriers are also presented. It turn ..."
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Summary. The explicit twostep RungeKutta (TSRK) formulas for the numerical so lution of ordinary differential equations are analyzed. The order conditions are derived and the construction of such methods based on some simplifying assumptions is described. Order barriers are also presented
Robust and reliable defect control for RungeKutta methods
 ACM Trans. Math. Soft
, 2007
"... The quest for reliable integration of initial value problems (IVPs) for ordinary differential equations (ODEs) is a longstanding problem in numerical analysis. At one end of the reliability spectrum are fixed stepsize methods implemented using standard floating point, where the onus lies entirely w ..."
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Cited by 5 (2 self)
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The quest for reliable integration of initial value problems (IVPs) for ordinary differential equations (ODEs) is a longstanding problem in numerical analysis. At one end of the reliability spectrum are fixed stepsize methods implemented using standard floating point, where the onus lies entirely
Results 1  10
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283,209