Statistics – Computation
Scientific paper
Nov 1999
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1999apnm...31..353v&link_type=abstract
Appl. Numer. Math. (Netherlands), Vol. 31, No. 3, p. 353 - 374
Statistics
Computation
Orbit Determination: Celestial Mechanics, Orbit Determination: Computing
Scientific paper
Many orbit problems in celestial mechanics are described by (nonstiff) initial-value problems (IVPs) for second-order ordinary differential equations of the form y″= f(y). The authors consider high-order parallel methods which fit into the class of general linear methods. In each step, these methods compute blocks of k approximate solution values (or stage values) at k different points using the whole previous block of solution values. The k stage values can be computed in parallel, so that on a k-processor computer system such methods effectively perform as a one-value method. The block methods considered in this paper are such that each equation defining a stage value resembles a linear multistep equation of the familiar Störmer-Cowell type. For k = 4 and k = 5 they constructed explicit PSC methods with stage order q = k and step point order p = k+1 and implicit PSC methods with q = k+1 and p = k+2. For k ≥ 6 one can construct explicit PSC methods with q = k and p = k+2 and implicit PSC methods with q = k+1 and p = k+3. It turns out that for k ≥ 5 the abscissae of the stage values can be chosen such that only k-1 stage values in each block have to be computed, so that the number of computational stages, and hence the number of processors and the number of starting values needed, reduces to k* = k-1.
de Swart J. B. J.
Messina Emanuele
van der Houwen P. J.
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