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Vietnam Journal of Mathematics 35:2(2007)
223-229
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Twostep-by-twostep PIRKC Methods
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Nguyen Huu Cong and
Le Ngoc Xuan
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Abstract. This paper concerns 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) PC
methods with continuous output formulas (twostep-by-twostep PIRKC methods
or TBTPIRKC methods) paralled-iterated RK-type PC methos with continuous
output for mulas (PIRKC method) give us a faster integration process.
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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2000 Mathematics Subject Classification: 65L05, 65L06.
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Keywords: Runge-Kutta methods, predictor-corrector
methods, stability, parallelism.
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Established
by Vietnam Academy of Science and Technology & Vietnam Mathematical
Society
Published
by Springer since January 2013
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