Global smooth solution curves using rigorous branch following

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 pse...

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Bibliographic Details
Published in:Mathematics of computation 2010-07, Vol.79 (271), p.1565-1584
Main Authors: VAN DEN BERG, JAN BOUWE, LESSARD, JEAN-PHILIPPE, MISCHAIKOW, KONSTANTIN
Format: Article
Language:English
Subjects:
A priori knowledge
Approximation
Banach space
Differential equations
Energy levels
Exact sciences and technology
Functional analysis
Geometric planes
Mathematical analysis
Mathematical independent variables
Mathematics
Methods of scientific computing (including symbolic computation, algebraic computation)
Numerical analysis
Numerical analysis. Scientific computation
Operator theory
Ordinary differential equations
Polynomials
Same sex marriage
Sciences and techniques of general use
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Summary: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.
ISSN:0025-5718
1088-6842
DOI:10.1090/S0025-5718-10-02325-2