Validation Continuation of Equilibria of PDEs
Chaotic Braided Solutions via Rigorous Numerics: Chaos in the Swift-Hohenberg Equations, J.B. van den Berg, J.-P. Lessard, Submitted, (2007). 

Validated Continuation Over Large Parameter Ranges for Equilibria of PDEs, M. Gameiro, J.-P. Lessard, K. Mischaikow, To appear in Mathematics and Computers in Simulation, (2007). 

Validated Continuation for Equilibria of PDEs, S. Day, J.-P. Lessard, K. Mischaikow, SIAM Journal on Numerical Analysis, 45 (4), 1398-1424, (2007). 

Code for the Validated Continuation for Equilibria of PDEs paper: 
http://www.math.gatech.edu/~lessard/continuation/cont_code