Global smooth solution curves using rigorous branch following

van den Berg, Jan; Lessard, Jean-Philippe; Mischaikow, Konstantin

doi:10.1090/S0025-5718-10-02325-2

Global smooth solution curves using rigorous branch following
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by Jan Bouwe van den Berg, Jean-Philippe Lessard and Konstantin Mischaikow;

Math. Comp. 79 (2010), 1565-1584

DOI: https://doi.org/10.1090/S0025-5718-10-02325-2

Published electronically: March 11, 2010

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Abstract:

In this paper, we present a new method for rigorously computing smooth branches of zeros of nonlinear operators $f:\mathbb {R}^{l_1} \times B_1 \rightarrow \mathbb {R}^{l_2} \times B_2$, 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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