Geodesic
The Parker--Sochacki method for solving systems of ordinary differential equations using graphics processors
Sibirskij žurnal vyčislitelʹnoj matematiki, Tome 14 (2011) no. 3, pp. 277-289

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In this paper we describe the Parker–Sochacki method, which is used for solving systems of ordinary differential equations and the implementation of this method on the graphics processors. As a test, we consider the solution of the classical $N$ bodies problem. The algorithm makes possible to effectively use massive parallel graphics processors, and provides an acceptable accuracy at a multiple time reduction as compared to the processors of a conventional architecture. 
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     author = {E. A. Nurminski and A. A. Bury},
     title = {The {Parker--Sochacki} method for solving systems of ordinary differential equations using graphics processors},
     journal = {Sibirskij \v{z}urnal vy\v{c}islitelʹnoj matematiki},
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E. A. Nurminski; A. A. Bury. The Parker--Sochacki method for solving systems of ordinary differential equations using graphics processors. Sibirskij žurnal vyčislitelʹnoj matematiki, Tome 14 (2011) no. 3, pp. 277-289. http://geodesic.mathdoc.fr/item/SJVM_2011_14_3_a3/