Twostep-by-twostep PIRK-type PC methods with continuous output formulas
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.
scientific article; zbMATH DE number 5355640