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Effective Realization of Numerical Integration Method for Stiff Problems
Author(s) -
Griepentrog E.,
Möbius A.
Publication year - 1985
Publication title -
zamm ‐ journal of applied mathematics and mechanics / zeitschrift für angewandte mathematik und mechanik
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.449
H-Index - 51
eISSN - 1521-4001
pISSN - 0044-2267
DOI - 10.1002/zamm.19850651112
Subject(s) - extrapolation , realization (probability) , stability (learning theory) , consistency (knowledge bases) , newton's method , numerical integration , trapezoidal rule , computer science , numerical analysis , mathematics , mathematical optimization , algorithm , mathematical analysis , nonlinear system , statistics , physics , quantum mechanics , machine learning , artificial intelligence
The theoretical part of this paper shows that, by means of a suitable chosen predictor, only one Newton iteration step is needed in order to get the desired consistency and stability properties of an implicit numerical integration method. Furthermore, an algorithm for this Newton step is suggested, whose effort depends only on the number of the stiff solution components. In the practical considerations the introduced principles are applied to a mixed extrapolation method based on the trapezoidal rule. Special cheap methods for the error estimation and stepsize control are developed.