A class of variable stepsize formulas for the parallel solution of ODE's

This paper adapts the general class of formulas, collectively known as the block predictor-corrector (BPC) formula to variable stepsize. These formulas are used to solve initial value problems in ordinary differential equations (ODE's) in parallel. The predictor formula within the BPC method contains a number of free parameters. Each selection of these parameters defines one member of the BPC class of formulas. Several choices for the values of the parameters have been proposed in the literature in a way to either reduce round-off errors or to increase the stability of the formulas. Other recent considerations have demonstrated superior characteristics and in order to conduct meaningful experimentation and testing on them, and also for reasons of efficiency, the corresponding formulas have to be implemented in variable stepsize. In this paper, the general BPC formula is adapted to variable stepsize for any arbitrary selection of the free parameters.