Optimally stable parallel predictors for Adams—Moulton correctors

AbstractThe stability properties of a class of predictor—corrector algorithms which are designed for parallel computation in the numerical solution of systems of ordinary differential equations are studied. It is shown that if the corrector is fixed to be an Adams—Moulton Corrector, then the optimally stable parallel predictor (in the sense that the parallel scheme has a maximum stability interval on the negative real axis) is the Adams—Bashforth predictor shifted to the right by one integration step. The size of the stability intervals on the negative real axis in optimally stable algorithms of various orders are compared with those of the standard serial Runge—Kutta and serial predictor—corrector methods. Corresponding stability regions in the complex plane are presented for fourth order algorithms and the results are illustrated by sample problems