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In this paper we describe various recent enhancements of the original method of computations with remainder bounds that allow the control of the errors made both by the integrator scheme and any possible inaccuracy of the description of the system.
Using suitable extensions of the DA and Taylor model operators used in the Schauder fixed point theorem formulation of the ODE problem leads to a very transparent approach for the calculation of enclosures for the intergration errors. Under the presence of a scheme for effective treatment of sparsity in the DA vectors, such as the method available in the code COSY INFINITY, the additional resources necessary for this algorithm are very modest.
M. Berz, K. Makino, Nuclear Instruments and Methods A519 (2004) 53-62
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