Runge-Kutta (RK) methods are often used for solving non-stiff initial-value problems (IVPs) for systems of first-order ordinary differential equations. With the goal to provide potential for parallel processing, this paper investigates a particular class of parallel iterated RK-type (PIRK-type) predictor-corrector (PC) methods based on continuous collocation RK corrector methods. At the $n$th step, the continuous output formulas are used for predicting the stage values for the PC iteration and for calculation the step value at the $(n+2)$th step, yielding a two-step by two-step integration process. A comparison with PIRK and PIRKC methods shows the efficiency of the new methods.
Reviewer: Thomas Rauber (Bayreuth)