Generalized Runge-Kutta methods of order four with stepsize control for stiff ordinary differential equations

Peter Kaps; Peter Rentrop

doi:10.1007/BF01396495

Generalized Runge-Kutta methods of order four with stepsize control for stiff ordinary differential equations

Peter Kaps, Peter Rentrop

Chair of Automotive Technology

University of Innsbruck

Research output: Contribution to journal › Article › peer-review

267 Scopus citations

Abstract

Generalized A(α)-stable Runge-Kutta methods of order four with stepsize control are studied. The equations of condition for this class of semiimplicit methods are solved taking the truncation error into consideration. For application an A-stable and an A(89.3°)-stable method with small truncation error are proposed and test results for 25 stiff initial value problems for different tolerances are discussed.

Original language	English
Pages (from-to)	55-68
Number of pages	14
Journal	Numerische Mathematik
Volume	33
Issue number	1
DOIs	https://doi.org/10.1007/BF01396495
State	Published - Mar 1979

Keywords

Subject classifications: AMS(MOS):65L05, CR:5.17

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10.1007/BF01396495

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abstract = "Generalized A(α)-stable Runge-Kutta methods of order four with stepsize control are studied. The equations of condition for this class of semiimplicit methods are solved taking the truncation error into consideration. For application an A-stable and an A(89.3°)-stable method with small truncation error are proposed and test results for 25 stiff initial value problems for different tolerances are discussed.",

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AB - Generalized A(α)-stable Runge-Kutta methods of order four with stepsize control are studied. The equations of condition for this class of semiimplicit methods are solved taking the truncation error into consideration. For application an A-stable and an A(89.3°)-stable method with small truncation error are proposed and test results for 25 stiff initial value problems for different tolerances are discussed.

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Generalized Runge-Kutta methods of order four with stepsize control for stiff ordinary differential equations

Abstract

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