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Adaptive Refinement of the Generalized Cell Mapping
Author(s) -
Guder R.,
Kreuzer E.
Publication year - 1999
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.19990791345
Subject(s) - computer science , nonlinear system , term (time) , dynamical systems theory , grid , mathematical optimization , nonlinear dynamical systems , mathematics , algorithm , geometry , physics , quantum mechanics
For the prediction of the long term behavior and global analysis of nonlinear dynamical systems the generalized cell mapping is an efficient and powerful numerical tool. The only drawback of this method is the enormous computational effort for higher‐dimensional systems. We overcome this problem by several adaptive refinement steps of a very rough starting cell grid, where the adaption is controlled by the long‐term dynamics of the system. We illustrate the efficiency by examples.