A smooth output interpolation process for BDF codes

摘要

The original line of codes developed and popularized by C.W. Gear and A.C. Hindmarsh (which use the backward differentiation formulae appropriate for solving stiff problems) produce discontinuous derivative approximations at all mesh points and discontinuous solution approximations at certain mesh points when a change in the order of the method takes place. We discuss the changes necessary to eliminate these discrepancies and define a globally smooth interpolation process. These improvements are particularly important in the context of defining a mathematically sound root solving algorithm.