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Global smooth solution curves using rigorous branch following


Authors: Jan Bouwe van den Berg, Jean-Philippe Lessard and Konstantin Mischaikow
Journal: Math. Comp. 79 (2010), 1565-1584
MSC (2010): Primary 37M99; Secondary 65G20, 65N30
DOI: https://doi.org/10.1090/S0025-5718-10-02325-2
Published electronically: March 11, 2010
MathSciNet review: 2630003
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Abstract: In this paper, we present a new method for rigorously computing smooth branches of zeros of nonlinear operators $ f:\mathbb{R}^{l_1} \times B_1 \rightarrow \re^{l_2} \times B_2$, where $ B_1$ and $ B_2$ are Banach spaces. The method is first introduced for parameter continuation and then generalized to pseudo-arclength continuation. Examples in the context of ordinary, partial and delay differential equations are given.


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Additional Information

Jan Bouwe van den Berg
Affiliation: VU University Amsterdam, Department of Mathematics, De Boelelaan 1081, 1081 HV Amsterdam, The Netherlands
Email: janbouwe@few.vu.nl

Jean-Philippe Lessard
Affiliation: Rutgers University, Department of Mathematics, Hill Center-Busch Campus, 110 Frelinghuysen Rd, Piscataway, New Jersey 08854-8019 and VU University Amsterdam, Department of Mathematics, De Boelelaan 1081, 1081 HV Amsterdam, The Netherlands
Email: lessard@math.rutgers.edu

Konstantin Mischaikow
Affiliation: Rutgers Univeristy, Department of Mathematics, Hill Center-Busch Campus, 110 Frelinghuysen Rd, Piscataway, New Jersey 08854-8019
Email: mischaik@math.rutgers.edu

DOI: https://doi.org/10.1090/S0025-5718-10-02325-2
Received by editor(s): September 29, 2009
Received by editor(s) in revised form: May 18, 2009
Published electronically: March 11, 2010
Additional Notes: The second author was supported in part by NSF Grant DMS-0511115, by DARPA, and by DOE Grant DE-FG02-05ER25711.
The third author was supported by NSF Grant DMS-0638131, DMS-0835621, DMS-0915019, DARPA, DOE Grant DE-FG02-05ER25711, and by AFOSR
Article copyright: © Copyright 2010 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.