Course details

Higly Sophisticated Computations

VND Acad. year 2016/2017 Summer semester

Current academic year

The course is aimed at practical methods of solving problems encountered in science and engineering: large systems of differential equations, algebraic equations, partial differential equations,stiff systems, problems in automatic control, electric circuits, mechanical systems, electrostatic and electromagnetic fields. An original method based on a direct use of Taylor series is used to solve the problems numerically. The course also includes analysis of parallel algorithms and design of special architectures for the numerical solution of differential equations. A special simulation language TKSL is available.

Guarantor

Kunovský Jiří, doc. Ing., CSc.

Language of instruction

Czech, English

Completion

Examination (written)

Time span

  • 39 hrs lectures
  • 26 hrs pc labs

Assessment points

  • 60 pts final exam (written part)
  • 20 pts mid-term test (written part)
  • 20 pts labs

Department

Department of Intelligent Systems (UITS)

Subject specific learning outcomes and competences

Ability to analyse the selected methods for numerical solutions of differential equations (based on the Taylor Series Method) for extremely exact and fast solutions of sophisticated problems.

  • An individual solution of a nontrivial system of diferential equations.

Learning objectives

To provide overview and basics of practical use of selected methods for numerical solutions of differential equations (based on the Taylor Series Method) for extremely exact and fast solutions of sophisticated problems.

Prerequisite knowledge and skills

Numerical Mathematics

Fundamental literature


    • Kunovský, J.: Modern Taylor Series Method, habilitační práce, VUT Brno, 1995
    • Vitásek,E.: Základy teorie numerických metod pro řešení diferenciálních rovnic. Academia, Praha, 1994.
    • Miklíček,J.: Numerické metody řešení diferenciálních úloh, skripta, VUT Brno,1992

Syllabus of lectures

  • Methodology of sequential and parallel computation (feedback stability of parallel computations)
  • Extremely precise solutions of differential equations by the Taylor series method
  • Parallel properties of the Taylor series method
  • Basic programming of specialised parallel problems by methods using the calculus (close relationship of equation and block description)
  • Parallel solutions of ordinary differential equations with constant coefficients
  • Adjunct differential operators and parallel solutions of differential equations with variable coefficients
  • Methods of solution of large systems of algebraic equations by transforming them into ordinary differential equations
  • Parallel applications of the Bairstow method for finding the roots of high-order algebraic equations
  • Fourier series  and finite integrals
  • Simulation of electric circuits
  • Solution of practical problems described by partial differential equations
  • Library subroutines for precise computations
  • Conception of the elementary processor of a specialised parallel computation system.

Progress assessment

Study evaluation is based on marks obtained for specified items. Minimimum number of marks to pass is 50.

Controlled instruction

Submission of report on the results of experiments carried out within the tutorial.

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