Course detail

Highly Sophisticated Computations

FIT-VNDAcad. year: 2017/2018

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.

Language of instruction

Czech

Mode of study

Not applicable.

Guarantor

doc. Ing. Jiří Kunovský, CSc.

Department

Department of Intelligent Systems (UITS)

Learning outcomes of the course unit

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.

Prerequisites

Numerical Mathematics

Co-requisites

Not applicable.

Planned learning activities and teaching methods

Not applicable.

Assesment methods and criteria linked to learning outcomes

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

Course curriculum

    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.

Work placements

Not applicable.

Aims

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.

Specification of controlled education, way of implementation and compensation for absences

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

Recommended optional programme components

Not applicable.

Prerequisites and corequisites

Not applicable.

Basic literature

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

Recommended reading

Not applicable.

Classification of course in study plans

  • Programme CSE-PHD-4 Doctoral

    branch DVI4 , 0 year of study, summer semester, elective