Abstract
We investigate the problem of how big would be the additional accuracy gain from a two-step bdf algorithm for ordinary differential equations if its weights are constructed via function fitting. We find that (i) the order of the algorithm is increased by three units (from two to five), (ii) this enhancement can be achieved not only in the frame of the traditional exponential fitting but also in the frame of a new, more general approach, which results more flexible and safer than the other one.
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