Some remarks on the intervals of stability of Runge-Kutta methods after Richardson extrapolation
A. Olejniczak (1987)
Applicationes Mathematicae
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A. Olejniczak (1987)
Applicationes Mathematicae
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M. Szyszkowicz (1985)
Applicationes Mathematicae
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M. Szyszkowicz (1987)
Applicationes Mathematicae
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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.
M.N. Spijker (1986/87)
Numerische Mathematik
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E. Hairer (1986)
Numerische Mathematik
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M. Szyszkowicz (1987)
Applicationes Mathematicae
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K. Strehmel, R. Weiner (1984)
Numerische Mathematik
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W.H. Hundsdorfer (1986/87)
Numerische Mathematik
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J.F.B.M. Kraaijevanger, J. Schneid (1991)
Numerische Mathematik
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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.
Marino Zennaro (1988)
Numerische Mathematik
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K. Strehmel, R. Weiner, J. Bruder (1987/88)
Numerische Mathematik
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