Efficient block predictor-corrector methods with a small number of corrections

AbstractRecently, various classes of predictor-corrector methods have been proposed as being suitable for solving nonstiff ordinary differential equations in a parallel environment. This paper shows that methods based on a low-order predictor and a Runge-Kutta corrector are not efficient and that if predictor-corrector methods are to be used efficiently for solving nonstiff problems in parallel, then high-order predictors are required. Examples of methods with high-order predictors are given and their efficiency properties are studied in terms of stability and local error theory