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 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
Improved parallel-iterated pseudo two-step RK methods for nonstiff IVPs
Applied Numerical Mathematics
A variable step implicit block multistep method for solving first-order ODEs
Journal of Computational and Applied Mathematics
Parallel Low-Storage Runge-Kutta Solvers for ODE Systems with Limited Access Distance
International Journal of High Performance Computing Applications
Euro-Par'12 Proceedings of the 18th international conference on Parallel Processing
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This paper deals with parallel predictor-corrector (PC) iteration methods based on collocation Runge-Kutta (RK) corrector methods with continuous output formulas for solving nonstiff initial-value problems (IVPs) for systems of first-order differential equations. At nth step, the continuous output formulas are used not only for predicting the stage values in the PC iteration methods but also for calculating the step values at (n+2)th step. In this case, the integration processes can be proceeded twostep-by-twostep. The resulting twostep-by-twostep (TBT) parallel-iterated RK-type (PIRK-type) methods with continuous output formulas (twostep-by-twostep PIRKC methods or TBTPIRKC methods) give us a faster integration process. Fixed stepsize applications of these TBTPIRKC methods to a few widely-used test problems reveal that the new PC methods are much more efficient when compared with the well-known parallel-iterated RK methods (PIRK methods), parallel-iterated RK-type PC methods with continuous output formulas (PIRKC methods) and sequential explicit RK codes DOPRI5 and DOP853 available from the literature.