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Optimization of Nordsieck's Method for the Numerical Integration of Ordinary Differential Equations
Author(s) -
Gmelig R. H. J.,
Traas C. R.
Publication year - 1984
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.19840640706
Subject(s) - equivalence (formal languages) , mathematics , ordinary differential equation , zero (linguistics) , truncation (statistics) , stability (learning theory) , truncation error , interval (graph theory) , linear multistep method , mathematical analysis , differential equation , statistics , computer science , differential algebraic equation , combinatorics , discrete mathematics , machine learning , linguistics , philosophy
Stability and accuracy of Nordsieck's integration method can be improved by choosing the zero‐positions of the extraneous roots of the characteristic equation in a suitable way. Optimum zero‐positions have been found by minimizing the lower bound of the interval of absolute stability and the coefficient of the truncation error. Various properties of the improved methods have been analysed, such as the behaviour of the high‐order terms, the equivalence with multistep methods and the damping of perturbations.