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Dive into the research topics where Reinhard Frank is active.

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Featured researches published by Reinhard Frank.


SIAM Journal on Numerical Analysis | 1981

The Concept of B-Convergence

Reinhard Frank; Josef Schneid; Christoph W. Ueberhuber

A useful concept of convergence for nonlinear stiff ODE’s will be developed, which permits the derivation of uniform global error bounds independent of the stiffness of the considered problem. This concept will be discussed for three simple methods for stiff systems, the implicit Euler scheme, the implicit midpoint rule and the implicit trapezoidal rule.


SIAM Journal on Numerical Analysis | 1985

Stability Properties of Implicit Runge–Kutta Methods

Reinhard Frank; Josef Schneid; Christoph W. Ueberhuber

New stability concepts—


Bit Numerical Mathematics | 1977

ITERATED DEFECT CORRECTION FOR THE EFFICIENT SOLUTION OF STIFF SYSTEMS OF ORDINARY DIFFERENTIAL EQUATIONS

Reinhard Frank; Christoph W. Ueberhuber

BS


Computing | 1978

Iterated defect correction for differential equations part I: theoretical results

Reinhard Frank; Christoph W. Ueberhuber

-stability and


Numerische Mathematik | 1989

Asymptotic error expansions for stiff equations: an analysis for the implicit midpoint and trapezoidal rules in the strongly stiff case

Winfried Auzinger; Reinhard Frank

BSI


Mathematics of Computation | 1977

An extension of the applicability of iterated deffered corrections

Reinhard Frank; Joerg Hertling; Christoph W. Ueberhuber

-stability (internal


SIAM Journal on Numerical Analysis | 1990

Asymptotic error expansions for stiff equations: the implicit Euler scheme

Winfried Auzinger; Reinhard Frank; F. Macsek

BS


Computing | 1983

The application of iterated defect correction to variational methods for elliptic boundary value problems

Reinhard Frank; J. Hertling; J. P. Monnet

-stability)—are introduced.


Computing | 1990

A note on convergence concepts for stiff problems

Winfried Auzinger; Reinhard Frank; Gabriela Kirlinger

BS


Journal of Computational and Applied Mathematics | 1993

Modern convergence theory for stiff initial-value problems

Winfried Auzinger; Reinhard Frank; Gabriela Kirlinger

-stability is a modification and extension of B-stability and enables the derivation of order results for Runge–Kutta methods applied to general nonlinear stiff initial value problems. These order results (B-consistency, B-convergence) are not affected by stiffness. Several classes of implicit Runge–Kutta methods are shown to be

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Christoph W. Ueberhuber

Vienna University of Technology

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Winfried Auzinger

Vienna University of Technology

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F. Macsek

Vienna University of Technology

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Gabriela Kirlinger

Vienna University of Technology

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Josef Schneid

Vienna University of Technology

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J. Hertling

Vienna University of Technology

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H. Lehner

Vienna University of Technology

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Hans J. Stetter

Vienna University of Technology

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J. P. Monnet

Vienna University of Technology

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