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- A New View of the computational complexity of IVP for ODE, August 25, 2001, Robert Corless, 8 pages
**Abstract**In this paper, in apparent contradiction to the standard theory of information-based complexity for the numerical solution of initial value problems for ordinary differential equations, I prove that adaption is better than non-adaption, and that there are algorithms of cost polynomial in the number of digits of accuracy requested, for the solution of IVP for ODE. Although I use some new methods, derived from a new result on equidistribution, the real reason these results are different from the standard theory is that I have modified the hypotheses of the standard theory. The standard theory of the computational complexity of the solution of IVP for ODE is correct as it stands, working from the standard hypotheses. However, it is my belief that the standard hypotheses, while plausible, are not good models of what happens in practice. What is observed in practice is that, generally, adaption is better than non-adaption, and that solution methods are efficient enough for practical purposes (and hence exponential cost is not a reasonable model). This paper should provoke some useful discussion, and perhaps further development of this neglected theory.UPDATED AUGUST 31, 2001

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