A smooth output interpolation process for BDF codes (Q1124291)

When using the original BDF (backward differentiation formulae) codes developed by C. W. Gear for solving stiff problems discontinuous derivative approximations result at all mesh points and discontinuous solution approximation are produced at certain mesh points when a change in the order of the method takes place. The author discusses the changes necessary to eliminate these discrepancies and the modifications in order to produce a globally smooth interpolation process. These improvements are particularly important in the context of defining a mathematically sound root algorithm. Numerical examples are included.