The analysis of parallel algorithms for the numerical decision of ordinary differential equations systems by Adams--Bachfort methods and Adams--Moulton methods

O. A. Dmitrieva

Matematičeskoe modelirovanie, Tome 12 (2000) no. 5, pp. 81-86.

Résumé

The realization of parallel algorithms for the decision of ordinary differential equations systems on computing structures with SIMD (Single Instruction Multiple Data) by architecture is considered. The numerical decision of a Cauchy problem for the ordinary differential equations systems with multiplying factors can be received consistently on steps with the help, for example, Adams–Bachfort formulas and Adams–Moulton formulas of the fourth order. At first under the Adams–Bachfort formula the values being the forecast are calculated. Then these meanings are used for account of the corrected meaning calculated with the Adams–Moulton formula. The models, by which the decision is guided, have the following features: the processors of SIMD structure with a square grid and a ruler of processor elements are used; each processor can execute any arithmetic operation for one step; the temporary expenses connected to the reference to the remembering device are absent. For estimations of the considered algorithms the most widespread criteria are used: factor of acceleration and efficiency.