Improved parallel-iterated pseudo two-step RK methods for nonstiff IVPs

Công, Nguyễn Hữu; Xuan, Le Ngoc

doi:10.1016/j.apnum.2006.11.005

Cited by 3 publications

(1 citation statement)

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“…Therefore, for a convenient comparison of various methods, we use the value of the quotient NCD/N seq which is called scaled accuracy (see also [14]). Then ignoring load balancing factors and communication times between processors in parallel methods, the numerical comparison of various methods in this section is based on the scaled accuracies.…”

Section: Numerical Comparisonsmentioning

confidence: 99%

Twostep-by-twostep PIRK-type PC methods with continuous output formulas

Công

Xuan

2008

Journal of Computational and Applied Mathematics

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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 (twostepby-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.

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Section: Numerical Comparisonsmentioning

confidence: 99%