Штучний інтелект

Анотація: Work is devoted to creation of parallel algorithms of integration step variable with the Cauchy problem for systems of the ordinary differential equations. Algorithms are under construction on multistep collocation blocks methods with the senior derivatives that provides vectorization of procedure of obtaining the decision. For alignment of an order of approximation in all settlement points of the block Hermite’s polynomials are used.

Ключові слова: Cauchy problem, parallel computing, collocation, Hermite’s polynomials

Посилання:

1. Dmitrieva O., Firsova A. Parallel Algorithms of Simulation. Increase of simulation of dynamic objects with the lumped pa rameters into parallel computer systems. – Lambert Academic Publishing, 2012. – 192 p.
2. Zanariah A. M., Suleiman M.B. Solving Large Systems of Ordinary Differential Equations on Parallel Computer // Journ. of Scientific Research. – 2009. – Vol. 29, № 4. – P. 491-501.
3. Feldman L., Nazarova I., Dmitrieva O., Mikhaylova T. Proceedings of DNTU. – 2010. – № 1. – P. 12-17.
4. Soderlind G. Digital filters in adaptive time-stepping // ACM Trans. Math. Soft. – 2003. – Vol. 29. – P. 1-26.
5. Dmitrieva O., Feldman L. Parallel Step Control. Development of parallel algorithms of the step variation for simulation of stiff dynamic systems. – Lambert Academic Publishing, 2013. – 72 p.
6. Firsova A, Dmitrieva O. Dynamic System Simulation. Robust algorithms of state estimation of dynamic lumped parameters systems. – Lambert Academic Publishing, 2011. – 92 p.
7. Dmitrievа O.A. Iskusstvennyj intellect. – 2012. – № 4. – S. 77-88.
8. Dmitrieva O.A. Radіoelektronnye komp'yuternye systemy. – 2012. – № 6 (58). – S. 312-317.
9. Hayrer E., Wanner. G. Solution of ordinary differential equations. Tough task. – Springer-Verlag, 1999. – 685s.
10. Dmitrieva O. A. Radіoelektronnye komp'yuternye systemy. – 2013. – № 5 (64). – S. 243-249.
11. Dmitrієva O. A. ІKOT. – 2011. – № 14 (188). – S. 36-43.
12. Arushanjan O.B., Zaljotkin S.F., Kalitkin N.N. Vychislitelnye metody I programmirovaniye. – 2002. – № 3. – S. 11-19.