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Generalized ROW-type methods for solving semi-explicit DAEs of index-1

  • A new type of Rosenbrock-Wanner (ROW) methods for solving semi-explicit DAEs of index-1 is introduced. The scheme considers arbitrary approximations to Jacobian entries resulting for the differential part and thus corresponds to a first attempt of applying W methods to DAEs. Besides, it is a generalized class covering many ROW-type methods known from literature. Order conditions are derived by a consistent approach that combines theories of ROW methods with exact Jacobian for DAEs (Roche, 1988) and W methods with arbitrary Jacobian for ODEs (Steihaug and Wolfbrandt, 1979). In this context, rooted trees based on Butcher’s theory that include a new type of vertices are used to describe non-exact differentials of the numerical solution. Resulting conditions up to order four are given explicitly, including new conditions for realizing schemes of higher order. Numerical tests emphasize the relevance of satisfying these conditions when solving DAEs together with approximations to Jacobian entries of the differential part.

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Metadaten
Document Type:Article
Language:English
Parent Title (English):Journal of Computational and Applied Mathematics
Volume:316
First Page:213
Last Page:228
ISSN:0377-0427
DOI:https://doi.org/10.1016/j.cam.2016.08.024
Publisher:Elsevier
Date of first publication:2016/09/06
Note:
Selected Papers from NUMDIFF-14
Tag:Approximated Jacobian; Differential-algebraic equations; Order conditions; Rosenbrock methods; W methods
Departments, institutes and facilities:Fachbereich Elektrotechnik, Maschinenbau, Technikjournalismus
Institut für Technik, Ressourcenschonung und Energieeffizienz (TREE)
Dewey Decimal Classification (DDC):5 Naturwissenschaften und Mathematik / 51 Mathematik / 510 Mathematik
Entry in this database:2016/09/20