The numerical analysis of ordinary differential equations: Runge-Kutta and general linear methods
The numerical analysis of ordinary differential equations: Runge-Kutta and general linear methods
Parallel solution of ODE's by multi-block methods
SIAM Journal on Scientific and Statistical Computing
Parallel iteration of high-order Runge-Kutta methods with stepsize control
Journal of Computational and Applied Mathematics
Solving ordinary differential equations I (2nd revised. ed.): nonstiff problems
Solving ordinary differential equations I (2nd revised. ed.): nonstiff problems
Parallel methods for initial value problems
Applied Numerical Mathematics - Special issue: parallel methods for ordinary differential equations
Efficient block predictor-corrector methods with a small number of corrections
Journal of Computational and Applied Mathematics - Special issue on numerical methods for ordinary differential equations
Parallel block predictor-corrector methods of Runge-Kutta type
Selected papers of the sixth conference on Numerical Treatment of Differential Equations
Parallel iteration of symmetric Runge-Kutta methods for nonstiff initial-value problems
Journal of Computational and Applied Mathematics
Parallel and sequential methods for ordinary differential equations
Parallel and sequential methods for ordinary differential equations
Continuous variable stepsize explicit pseudo two-step RK methods
Journal of Computational and Applied Mathematics
Twostep-by-twostep PIRK-type PC methods with continuous output formulas
Journal of Computational and Applied Mathematics
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The aim of this paper is to consider a parallel predictor-corrector (PC) iteration scheme for a general class of pseudo two-step Runge-Kutta methods (PTRK methods) of arbitrary high-order for solving first-order nonstiff initial-value problems (IVPs) on parallel computers. Starting with an s-stage pseudo two-step RK method of order p^* with w implicit stages, we apply a highly parallel PC iteration process in PE(CE)^mE mode. The resulting parallel PC method can be viewed as a parallel-iterated pseudo two-step Runge-Kutta method (PIPTRK method) with an improved (new) predictor formula and therefore will be called the improved PIPTRK method (IPIPTRK method). The IPIPTRK method uses an optimal number of processors equal to w=