Jan has been working on an implementation of the C^1-Lohner ODE-IVP solver described previously. As a first step he has been considering various ways to implement Taylor methods for ODEs, and following the advice of Barrio's
Performance of the Taylor series method for ODEs/DAEs Jan decided to use a recursive scheme based on automatic differentiation. This is also the scheme suggested by Zgliczynski in the paper describing the Lohner algorithm itself. The correct choice of algorithm for this sub-procedure of the solver is crucial as the computation if performed in each time-step. Ideally as much as possible of the computation should be performed at initialization, when the field of the IVP is first identified and Jan will be keeping in mind choices that will keep this a possibility.
