Extending convergence of BDF methods for a class of nonlinear strongly stiff problems

In 1995, a new approach was presented to overcome the drawbacks of existing convergence theory for stiff initial value problems by Auzinger et al. (BIT 36 (4) (1996) 635–652), and illustrated by means of a convergence argument for the implicit Euler scheme. In the present paper, our intention is to obtain extending quantitive convergence results of BDF methods for a class of nonlinear strongly stiff problems and to illustrate further this new approach. Some numerical examples confirm our results.