On a Newton-Type Method for Differential-Algebraic Equations
Joint Authors
Legaz, M. J.
Pedregal, P.
Amat, S.
Source
Journal of Applied Mathematics
Issue
Vol. 2012, Issue 2012 (31 Dec. 2012), pp.1-15, 15 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2012-12-24
Country of Publication
Egypt
No. of Pages
15
Main Subjects
Abstract EN
This paper deals with the approximation of systems of differential-algebraic equations based on a certain error functional naturally associated with the system.
In seeking to minimize the error, by using standard descent schemes, the procedure can never get stuck in local minima but will always and steadily decrease the error until getting to the solution sought.
Starting with an initial approximation to the solution, we improve it by adding the solution of some associated linear problems, in such a way that the error is significantly decreased.
Some numerical examples are presented to illustrate the main theoretical conclusions.
We should mention that we have already explored, in some previous papers (Amat et al., in press, Amat and Pedregal, 2009, and Pedregal, 2010), this point of view for regular problems.
However, the main hypotheses in these papers ask for some requirements that essentially rule out the application to singular problems.
We are also preparing a much more ambitious perspective for the theoretical analysis of nonlinear DAEs based on this same approach.
American Psychological Association (APA)
Amat, S.& Legaz, M. J.& Pedregal, P.. 2012. On a Newton-Type Method for Differential-Algebraic Equations. Journal of Applied Mathematics،Vol. 2012, no. 2012, pp.1-15.
https://search.emarefa.net/detail/BIM-1028984
Modern Language Association (MLA)
Amat, S.…[et al.]. On a Newton-Type Method for Differential-Algebraic Equations. Journal of Applied Mathematics No. 2012 (2012), pp.1-15.
https://search.emarefa.net/detail/BIM-1028984
American Medical Association (AMA)
Amat, S.& Legaz, M. J.& Pedregal, P.. On a Newton-Type Method for Differential-Algebraic Equations. Journal of Applied Mathematics. 2012. Vol. 2012, no. 2012, pp.1-15.
https://search.emarefa.net/detail/BIM-1028984
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-1028984