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Using numerical experiments to discover theorems in differential equations

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.