Magistracy Department of Donetsk National Technical University

Computer science faculty

Department of applied mathematics and informatics

Abstract of Thesis

Introduction

Matrix-vector operation (MVO)

MVO characteristics

Runge-Kutta method

Ordinary differential equations (ODE)

ODE Iterative solving method

Acceleration via Newton method

ODE systems solving

Conclusions

Literature

Automated systems software specialty

Abstract of Thesis

"Parallel computational methods of Cauchy problem solving for the ordinary differential equation systems"

Russian version

CONCLUSIONS

As the result of theoretical analysis next information was concluded:

  1. On the basis of the offered theoretical communication model and computing system architecture features comparative analysis of parallel matrix-vector calculation algorithms has been lead.
  2. On the basis of the item (1) result and parallel algorithms for the linear ODE systems Cauchy problem solving on SIMD computer systems [2] suitable block parallel algorithms for matrix–vector multiplication have been offered and investigated.
  3. On the basis of a material [5] parallel algorithm for the ODE system Cauchy problem solving has been offered and investigated for a fixed parameters of problem and computer system topology.

In prospective further researches practical characteristics of performance of offered algorithms implementations on the computing system considered topology will be investigated. As priority task the finding-out problem of adequacy of theoretical characteristics conformity of the offered communication model and practical parameters for the investigated algorithms and the computing system is considered.

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