(1) School of Computational and Applied Mathematics, University of the Witwatersrand, Private Bag 3, Wits, 2050, Johannesburg, South Africa
Abstract:
In recent papers the technique for a local and global error estimation and the local-global step size control were presented
to solve both ordinary differential equations and semi-explicit index 1 differential-algebraic systems by multistep methods
with any reasonable accuracy attained automatically. Now those results are extended to the concept of multistep extrapolation,
and the paper demonstrates with numerical examples how such methods work in practice. Especially, we develop an efficient
technique to calculate higher derivatives of a numerical solution with Hermite interpolating polynomials. The necessary theory
is also provided.
AMS subject classification (2000) 65L06, 65L70, 65L80