This work explores the use of numerical experiments in two specific
cases: (1) the discovery of two families of exact solutions to the elastic
string equations, and approximately periodic solutions that appear to exist
near pseudo-solutions formed from these families; (2) the study of the
diffusion-reaction-conduction process in an electrolyte wedge (meniscus corner)
of a current-producing porous electrode. This latter work establishes the
well-posedness of the electrolyte wedge problem and provides asymptotic expansions
for the current density and total current produced by such a wedge.
The theme of this paper is the use of computing to discover a result that is
difficult or impossible to find without a computer, but which once observed,
can then be proven mathematically.