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Extra info for Continuation and Bifurcations: Numerical Techniques and Applications
10 compared with the shape of the unstable cycle (C). The kinetic variable u is the time dependent relative temperature, (T-TO)ITO' with respect to the ambient temperature (TO) reported in the left column. The even penods are located beyond the homoclinic tangency and the odd periods below.
Temam (1989), Nonlinear Galerkin methodll, SIAM J. Numer. , 26, pp. 1139-1157. Michelson, D. (1986), SteadYllolutionil of the Kuramoto-Sivallhinllky equation, Physica, 19D, pp. 89-111. Nicolaenko, B. , 1987, C. Foias, B. Nicolaenko, and R. Temam eds. Contemporary Mathematics (to appear). , B. Scheurer, R. Temam (1989), Some global dynamical propertiell of a clasll of pattern formation equations, Commun. in Partial Differential Equations, 14, pp. 245-297. Orszag, S. A. (1971), Numericaillimulation of incomprellilible flowil within lIimple boundaries: Accuracy, J.
A promising research direction is the application of AIMs in the context of finitedifference approximations. Foias, Temam and Titi are currently developing schemes along these lines [Foias et al. (1989c)]. This may prove particularly appropriate for problems like (RDE), where aliasing errors are significant. Acknowledgements. S. Army Research Office through the Mathematical Sciences Institute of Cornell University. J) was visiting the Institute for Mathematics and its Applications at the University of Minnesota.