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Nowadays a rapid advancement of science and, especially, increasing of complexity of real-world problems are
taking place. In almost all cases solving of such problems is joined with critical material and computational costs
if even real. Minimum time overhead is the main constrain of the problem solving process. Using of
the high–performance computational algorithms implementation is needed in these cases.
The most part of the problems with high complexity (for example, modeling of the dynamic systems with the large
quantity of parameters) are reduced to the differential equations and its systems.
For the solving of higher order differential equations high–performance parallel computer systems are used. The most popular
of these are MIMD computers. According to the Flynn classification two classes of MIMD computer systems are marked
out [1, c. 29-33]: distributed memory computers and shared–memory computers.
Shared–memory computer systems show the lowest communicational overhead in the communicational operations. But
they are very expensive. On the one hand, distributed memory computer systems are characterized by the high
communicational overhead in the communicational operations. On the other hand, distributed memory computer systems
are good scalable. Growth of the quantity of the computational units must be complemented with the appropriate
communicational environment. Scalability value of shared–memory systems is hardware limited.
In order to achieve the highest possible performance the quantity of computer system’s features have to be taken in account.
Other important point in parallel algorithm choosing is relation of the problem being solved and its mathematical nature.
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