The application of a class of one-step methods to solve the initial value problem

M. Szyszkowicz

Displaying similar documents to “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.

Two one-step methods to solve the initial value problem

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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Algorithms 91-92. Two one-step methods with a given parameter

M. Szyszkowicz (1987)

Applicationes Mathematicae

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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.

On the Order Conditions of Runge-Kutta Methods with Higher Derivatives.

E. Gekeler, R. Widman (1986/87)

Numerische Mathematik

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Natural Runge-Kutta and Projection Methods.

Marino Zennaro (1988)

Numerische Mathematik

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Monotonicity and Boundedness in Implicit Runge-Kutta Methods.

M.N. Spijker (1986/87)

Numerische Mathematik

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Time discretizations for evolution problems

Miloslav Vlasák (2017)

Applications of Mathematics

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The aim of this work is to give an introductory survey on time discretizations for liner parabolic problems. The theory of stability for stiff ordinary differential equations is explained on this problem and applied to Runge-Kutta and multi-step discretizations. Moreover, a natural connection between Galerkin time discretizations and Runge-Kutta methods together with order reduction phenomenon is discussed.