ABSTRACT
Abstract All DE system applications fall into three sub-sets: IVP, BVP, ABVP. Author has three decades of numerics, mostly with a new solver [1] which converts any DE system into IVPs for Volterra IEs of second kind via simple, formal integration. Lorenz' primordial work [2], establishing "chaos" as a field of inquiry, was used as example in a course. Attempts to reproduce his results had mixed results; qualitative agreement was good but number and location of zero-crossings past instability (t ~ 17) disagreed. An integral solver [1] used step sizes from 0.01 [2] to 5 x 10~7. Reducing step size until changes are minimal did not work; the solution kept changing, suggesting a Heisenberglike "Uncertainty Principle" for certain numerics, "One crunches numbers, not for their sake, but to gain insights." (von Neumann). Results are summarized and ongoing work indicated, mostly improved quadratures (high-level Romberg). Current approach is numerical; analysis is minimal. Presumably, the differences were due to "modern" computers vis-a-vis 1960 machines and, possibly, to different methodologies; Lorenz used FDM; this uses an integral solver. Resolution of this discrepancy had to await more powerful computers recently available, namely Intel's P6 chip at 200 MHz used here.
