ABSTRACT
During the last years, several types of parallel methods for integrating non-stiff initial-value problems for first-order ordinary differential equation have been proposed. The majority of them are based on an implicit multistage method in which the implicit relations are solved by the predictor-corrector (or fixed point iteration) method. In the predictor-corrector approach the computation of the components of the stage vector iterate can be distributed over s processors, where s is the number of implicit stages of the corrector method. However, after each iteration, the processors have to exchange their just computed results. Given that the communication time between the processors is several orders greater that the computational time, this frequent communication between the processors is a serious drawback. Particularly on distributed memory computers, such a fine grain parallelism is not attractive. An alternative approach is based on implicit multistage methods which are such that the implicit stages are already parallel, so that they can be solved independently of each other. This means that only after completion of a step, the processors need to exchange their results. The purpose of this paper is the design of a class of parallel General Linear Methods for solving non-stiff Initial Value Problems. Since we are designing methods for non-stiff problems, the shape of the stability region will not be of concern in this work.
