Artificial intelligence

Abstract: The paper deals with the algorithm of the Newton method for solving nonlinear systems (NLS) and the fourth-order Runge-Kutta method for solving Cauchy problems for systems of ordinary differential equations (SODE) on multi-core computers with Intel Xeon Phi processors. In the development of algorithms, a multi-level model of parallel computing was used and features of the architecture of the multi-core computer were taken into account. Times required for the solving of various order SNE and SODE are given; acceleration and performance coefficients characterizing the employment of methods being proposed are evaluated, as well.

Keywords:

References:

1. Intel Xeon Phi Coprocessor System SoftwareDevelopers Guide, revision 2.03. – 2012. – p. 201.
2. Intel Xeon Phi [Elektr. Resurs]. – Rezhym dostupu:https://www.intel.com/content/www/us/en/products/processors/xeon-ph
3. Nesterenko A.N., Himich A.N., Yakovlev M.F.(2006) Nekotoryie voprosyi resheniya sistemnelineynyih uravneniy na mnogoprotsessornyihvyichislitelnyih sistemah s raspredelennoy pamyatyu.Vestnik kompyuternyih i informatsionnyihtehnologiy, M.: 2006.  № 10.  S. 54-56.
4. Yakovlev M.F., Herasymova T.O., Nesterenko A.N.(2009) Osoblyvosti rozviazuvannia systemneliniinykh ta dyferentsialnykh rivnian naparalelnykh kompiuterakh. Pytannia optymizatsiiobchyslen (POO – XXXV). Pratsi mizhnarodnohosympoziumu. – Kyiv: Instytut kibernetyky im. V.M.Hlushkova NAN Ukrainy, 2009. – T.2.– S. 435-439.
5. Himich A.N., Yakovlev M.F., Gerasimova T.A.(2007) Nekotoryie voprosyi resheniya sistemobyiknovennyih differentsialnyih uravneniy na MIMD-kompyuterah Kibernetika i sistemnyiyanalIz. (2), 175-182.