Journal of Computational and Applied Mathematics
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
Solving ordinary differential equations I (2nd revised. ed.): nonstiff problems
Solving ordinary differential equations I (2nd revised. ed.): nonstiff problems
Note on the performance of direct and indirect Runge-Kutta-Nystro¨m methods
Journal of Computational and Applied Mathematics
Explicit, high-order Runge-Kutta-Nystro¨m methods for parallel computers
Selected papers of the sixth conference on Numerical Treatment of Differential Equations
Parallel and sequential methods for ordinary differential equations
Parallel and sequential methods for ordinary differential equations
Explicit pseudo two-step RKN methods with stepsize control
Applied Numerical Mathematics
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This paper investigates parallel predictor-corrector (PC) iteration schemes based on direct collocation Runge-Kutta-Nystrom (RKN) corrector methods with continuous output formulas for solving nonstiff initial-value problems (IVPs) for systems of special second-order differential equations y^''(t)=f(t,y(t)). Consequently, the resulting parallel-iterated RKN-type PC methods are provided with continuous output formulas. The continuous numerical approximations are also used for predicting the stage values in the PC iteration processes. In this way, we obtain parallel PC methods with continuous output formulas and high-order predictors. Applications of the resulting parallel PC methods to a few widely-used test problems reveal that these new parallel PC methods are much more efficient when compared with the parallel-iterated RKN (PIRKN) methods and the sequential ODEX2 and DOPRIN codes from the literature.