The application of a class of one-step methods to solve the initial value problem
M. Szyszkowicz (1987)
Applicationes Mathematicae
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Displaying similar documents to “Two one-step methods to solve the initial value problem”
The application of a class of one-step methods to solve the initial value problem
The convergence of explicit Runge-Kutta methods combined with Richardson extrapolation
Faragó, István, Havasi, Ágnes, Zlatev, Zahari
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Runge-Kutta methods are widely used in the solution of systems of ordinary differential equations. Richardson extrapolation is an efficient tool to enhance the accuracy of time integration schemes. In this paper we investigate the convergence of the combination of any explicit Runge-Kutta method with active Richardson extrapolation and show that the obtained numerical solution converges under rather natural conditions.
Generalized Runge-Kutta Methods of Order Four with Stepsize Control for Stiff Ordinary Differential Equations.
P. Rentrop, P. Kaps (1979)
Numerische Mathematik
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Algorithms 91-92. Two one-step methods with a given parameter
M. Szyszkowicz (1987)
Applicationes Mathematicae
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Some remarks on the intervals of stability of Runge-Kutta methods after Richardson extrapolation
A. Olejniczak (1987)
Applicationes Mathematicae
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Partitioned Runge-Kutta Methods with Stiffness Detection and Stepsize Control.
Peter Rentrop (1985)
Numerische Mathematik
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The intervals of stability of Runge-Kutta methods after Richardson extrapolation
M. Szyszkowicz (1985)
Applicationes Mathematicae
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Fifth-order Runge-Kutta with higher order derivative approximations.
Goeken, David, Johnson, Olin (1999)
Electronic Journal of Differential Equations (EJDE) [electronic only]
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Partitioned Adaptive Runge-Kutta Methods for the Solution of Nonstiff and Stiff Systems.
K. Strehmel, R. Weiner, J. Bruder (1987/88)
Numerische Mathematik
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On the unique solvability of the Runge-Kutta equations.
J.F.B.M. Kraaijevanger, J. Schneid (1991)
Numerische Mathematik
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Order conditions for partitioned Runge-Kutta methods
Zdzisław Jackiewicz, Rossana Vermiglio (2000)
Applications of Mathematics
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We illustrate the use of the recent approach by P. Albrecht to the derivation of order conditions for partitioned Runge-Kutta methods for ordinary differential equations.