A class of implicit advanced step-point methods with a parallel feature for the solution of stiff initial value problems

In this paper, a class of implicit advanced step-point methods that possesses a parallel feature is presented. Their accuracy and stability characteristics are examined in some detail and an experimental nonparallel code has been developed in order to give us a fair indication of their capabilities. Our aim is not to discuss a “parallel implementation” but, to demonstrate the worthiness of the new methods. The experimental code is compared with the powerful MEBDF code on the stiff DETEST problem set and the statistics displayed are obtained from the DETEST evaluation package. Some initial conclusions concerning the efficiency of the new methods are drawn from the analysis of the numerical results.