Introduction

The computing capacity of computers actively grows, per era of information technologies. Requirement of mankind to the decision of more and more complex of tasks in parallel grow also. For example, decision of systems of the differential equations, systems of the linear algebraic equations, decision of the columns and others. The distributed and parallel calculations are integral in the decision of complex tasks.

In the world there is a plenty of ways of construction of the distributed models for the decision of set forth above tasks. It is such, as GRID-technologies, cluster systems, parallel programs with use of libraries MPI and Open MP, and such as technologies from Microsoft COM and DCOM, CORBA, OLE and ActiveX.

In master's work the rate on DCOM and decision of the differential equations is made.

Problem (urgency, purposes and objectives)

The necessity of use of the distributed approach to the decision of the differential equations is called by, that at account of the complex equation or at a plenty fine are necessary are to carried out by set of iterations, and the limitation of resources by one ПК requires many forces and time for their decision.

The urgency of such task in modern designing of complex dynamic systems, processing of a different sort of physical parameters, accounts of space devices and other has the large meaning, both for scientific, and for practical application. And the question of speed optimization of decision complex tasks is most popular at construction of the distributed computer systems and development of software to them.

The developed system should have an opportunity of account of the differential equations by means of a local network by one of several numerical methods. Should have an opportunity of account algorithm choice, of modes choice, of network interaction clients with a server and other parameters for increase system effectiveness.

Analysis of problem (Review and analysis of the basic researches and development)

There is an equation of a kind:

y' = f(x, y)
y(x0) = y0

It is a simple differential equation of the first order with one entry condition. Is present in view of definition curve through its derivative in a coordinate plane XY, under its numerical decision. Generally to equation satisfies family of curves, and the entry condition allows to choose from family of curves only one curve, which passes through the given point. The decision will be function of a kind y=f (x), and the numerical meaning of function is defined by a choice of argument and presence of numerical meaning of function.

There are two wide classes of methods of the decision:

  1. One-step methods. They are straight linees (without iterations), but require(demand) repeated repeated functions evaluations. It is difficult to estimate an admitted mistake of accounts.
  2. Multistage methods. Indirect, without repeated function evaluation, but for achievement of sufficient accuracy the iterations are required. The mistake of a method can be received as a result of calculations.

The reasonable combination of these two classes, taking into account their advantages and lacks, will allow finding the optimum effective decision.

The set forth above methods are generalized for the decision of the differential equations of the first order, and the equations of higher orders are reduced to systems of the equations of the first order.

Programmatic model

The program model is submitted as DCOM architecture. The main process (is carried out on a server), accepts the initial data from the user, previously having processed them. Then its creates the quantity, given by the user, of affiliated processes or clients, which will decide of task, whether it be the whole differential equation or its part, all depends on a degree of granularity chosen by the user. The main process sends initial data, the affiliated processes to make operations and return result. The accuracy of the decision by the received result is calculated, if the method allows to make such estimation, and if necessary process of calculations repeats. Result of calculations visualize in a program environment of a server.

In figure 1 such model of the decision of a task is given.

Figure 1. Parallel model
Figure 1. Parallel model (10 frames, 17 sec (3 + 1,25*8 + 4), animation)

The realization of component system occurs for the bill open-source of library GALA for environment of development in Delphi.

Executed and planed development and researches

The development of the distributed software have started from the analysis both choice of technology and task for research, then drawing up of architecture and analysis of algorithms of the decision of the differential equations.

On the present moment the following is ready:

  • the concept of software and specification of its basic modules;
  • is planned functionality of system of the decision of the differential equations;
  • four numerical methods of the decision and, accordingly, four algorithms of the decision of the differential equations on one PC, monolithic application are realized;
  • the results of job of these four applications and estimation of efficiency them are investigated.

Is planned to spend the following development and researches:

  • to develop component program system under the specification COM;
  • to develop the graphic user interface (GUI);
  • to transfer algorithms in компонентную environment and to debug network interaction;
  • to investigate efficiency of algorithms in a network, by means of experiments, to execute the comparative analysis and experts reports.

Conclusion

The realization of component-guided system of account of the differential equations will allow the scientists and experts to optimize efficiency of the work, to save time and to receive exact result.

Further it is possible to continue development of this project and to transfer it on other platforms, such as UNIX, Macintosh. In it the foreign manufacturers, for example The Open Group are engaged.

Also it is possible add new functionalities and new mathematical tasks requiring distributed calculation in this system, thus having expanded a product.

Literature

  1. Andrew S. Tanenbaum, Maarten van Steen.
    Distributed systems. Principles and paradigms.
  2. The decision of systems of the ordinary differential equations.
  3. V.P. Gergel, R.G. Strongin.
    Bases of parallel calculations for multiprocessor computing systems. The manual. Nizhni Novgorod, 2003.
  4. Elmanova, Trepalin, Tender.
    Delphi and COM.
  5. XIV. The electronic directory on interfaces, structures and functions used in COM.
  6. A.I. Mikov , E.B. Zamyatina.
    Distributed systems and algorithms.
  7. V.A. Kryukov.
    Distributed operation systems.
  8. William Woolsey Johnson.
    A treatise on ordinary and partial differential equations.