Global smooth solution curves using rigorous branch following
Jan Bouwe van den Berg, Jean-Philippe Lessard, Konstantin Mischaikow · Mathematics of Computation · 2010
In this paper, we present a new method for rigorously computing smooth branches of zeros of nonlinear operators f : R l 1 × B 1 → R l 2 × B 2 f:\mathbb {R}^{l_1} \times B_1 \rightarrow \mathbb {R}^{l_2} \times B_2 , where B 1 B_1 and B 2 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.