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Global smooth solution curves using rigorous branch following
Author(s):
Jan
Bouwe
van den Berg;
Jean-Philippe
Lessard;
Konstantin
Mischaikow.
Journal:
Math. Comp.
79
(2010),
1565-1584.
MSC (2010):
Primary 37M99;
Secondary 65G20, 65N30
Posted:
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  , where  and  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:
10.1090/S0025-5718-10-02325-2
PII:
S 0025-5718(10)02325-2
Received by editor(s):
September 29, 2009
Received by editor(s) in revised form:
May 18, 2009
Posted:
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
Copyright of article:
Copyright
2010,
American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.
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