Course detail

Higly Sophisticated Computations

FIT-VNDAcad. year: 2019/2020

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.

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.

Recommended optional programme components

Not applicable.

Recommended or required reading

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

Planned learning activities and teaching methods

Not applicable.

Assesment methods and criteria linked to learning outcomes

Not applicable.

Language of instruction

Czech, English

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.

Classification of course in study plans

  • Programme VTI-DR-4 Doctoral

    branch DVI4 , any year of study, summer semester, 0 credits, optional

  • Programme VTI-DR-4 Doctoral

    branch DVI4 , any year of study, summer semester, 0 credits, optional

  • Programme VTI-DR-4 Doctoral

    branch DVI4 , any year of study, summer semester, 0 credits, optional

  • Programme VTI-DR-4 Doctoral

    branch DVI4 , any year of study, summer semester, 0 credits, optional

Type of course unit

 

Lecture

39 hours, optionally

Teacher / Lecturer

Syllabus


  • 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.

Computer exercise

26 hours, compulsory

Teacher / Lecturer

eLearning