Global smooth solution curves using rigorous branch following

In this paper, we present a new method to rigorously compute smooth branches of zeros of nonlinear operators f : R1 × B1 → R2 × B2, where B1 and B2 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.