Scientific and Technical Journal


ISSN Print 2221-3937
ISSN Online 2221-3805
Development of software applications for modeling of dynamic systems based on multi-core and hyper-threading architecture of processors can provide significant performance benefits. In practical application programming, including solution of ordinary differential equations, the sequential methods of integration are dominated.
A plurality of parallel integration methods often remains a subject of scientific research without the widespread introduction to the practical applications.
The paper proposes parallel realization of the four-point block one-step integration method, built on basis multi-threading mechanism of Java. The ability to perform iterations independently in four points of block allows to parallelize the process of integration on four individual program threads.
If there are four processor cores, each of the threads may be performed on a single core, whereby it is theoretically possible to achieve a four-fold speedup of solving the problems. Significant speedup can also be obtained with a smaller number of cores on processors that have the hyper-threading technology. However, the data exchange between the threads and their synchronization require an additional time and then practical speedup is always less than the theoretical. It is shown that the effectiveness of multi-threaded realization of the block method of integration with blocking queue for data exchanges and synchronization of threads essentially depends on the amount of computation of the equation’s right side.
The correctness of parallel algorithm realization is verified on solving of the mildly stable and stiff problems. The conditions of effectiveness of multi-threaded realization are confirmed experimentally on solving a series of problems with varying degrees of the computational complexity of the differential equations right sides.
The discussed results can be used for estimation of the necessity and the possibility of using the parallel methods of integration and their multi-threaded realizations.
1. Herlihy M., and Shavit N., (2008), The art of Multiprocessor Programming. San Francisco, CA, USA: Morgan Kaufmann Publishers Inc., 508 p. ISBN 0123705916 9780123705914. (In English).
2. Ekhter SH., and Roberts DZH., Mnogo-yadernoe programmirovanie, [Multi-Core Pro-gramming: Increasing Performance through Software Multi-Threading], (2010), St. Peter-burg, Russian Federation, Piter Publ., 316 p. (In Russian).
3. Fel'dman L. P., and Dmitrieva O. A., Effektivnye metody rasparallelivaniya chislennogo resheniya zadachi Koshi dlya obyknovennykh differentsial'nykh uravnenij. [Effective Methods of Parallelization of the Numerical Solution of the Cauchy Problem for Ordinary Differential Equations], (2001), Matematicheskoe Modelirovanie, Moscow, Russian Federation, Vol. 13(7), pp. 66 – 72 (In Russian).
4. Ivens D. (ed.) Sistemy parallel'noi obrabotki [Parallel Processing Systems], (1985), Moscow, Russian Federation, Mir Publ., 416 p. (In Russian).
5. Horstmann C.S., and Cornell G., (2004), Core Java, Volume II Advanced Features. 7th ed. New Jersey: Prentice Hall, 1024 p.,
ISBN 0-13-111826-9 (In English).
6. Abubakar M.B., Ali M.B., and Muktar I. B., (2014), Formulation of ‘Predictor-Corrector’ Methods From 2-Step Hybrid Adams Methods for the Solution of Initial Value Problems of Ordinary Differential Equations, International Journal of Engineering and Applied Sciences, 5(3), pp. 9 –13 (In English).
7. Muhammad R., and Yahaya Y.A., (2012), A Sixth Order Implicit Hybrid Backward Differ-entiation Formulae (HBDF) for Block Solution of Ordinary Differential Equations, American Jour-nal of Mathematics and Statistics, 2(4), pp. 89 – 94, doi: 10.5923/j.ajms.20120204.04 (In English).
8. Popov G., Mastorakis N., and Mladenov V., (2010), Calculation of the Acceleration of Parallel Programs as a Function of the Number of Threads, In: Proceeding ICCOMP'10 Pro-ceedings of the 14th WSEAS international con-ference on Computers – Volume II, 2010, pp. 411 – 414, ISBN: 978-960-474-213-4 (In Eng-lish).
9. Goetz B, (2004), Java theory and Prac-tice: Dynamic Compilation and Performance Measurement – The perils of Benchmarking un-der Dynamic Compilation. IBM Developer Works. Available from: developerworks/ library/j-jtp12214/. (Accessed 16.11.14) (In English).
10. Georges A., Buytaert D., and Eeckhout L., (2007), Statistically Rigorous Java Perform-ance Evaluation. In: Proceedings of the 22nd Annual ACM SIGPLAN Conference on Object-Oriented Programming, Systems, Languages and Applications, pp. 57 – 78 (In English).
Last download:
2017-11-17 05:12:46

[ © KarelWintersky ] [ All articles ] [ All authors ]
[ © Odessa National Polytechnic University, 2014. Any use of information from the site is possible only under the condition that the source link! ]