Switching between modified Newton and fix-point iteration for implicit ode-solvers

In this paper we discuss the automatic switch between modified Newton iteration with the Jacobian not equal zero and fix-point iteration, i.e. the Jacobian equal zero. The switching strategy is based on the ratio between the norm of the displacement and the norm of the residual. Several examples are discussed both from non-stiff and stiff systems. These examples show that our strategy is working as predicted.This work was supported by NATO Research Grant Programme, project RG 096.80 and by National Sciences and Engineering Research Council of Canada, Grants: A1244, A3597, A4076, A8111, A8239, A8639.