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
Mode of study
Guarantor
Department
Learning outcomes of the course unit
- An individual solution of a nontrivial system of diferential equations.
Prerequisites
Co-requisites
Planned learning activities and teaching methods
Assesment methods and criteria linked to learning outcomes
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
Aims
Specification of controlled education, way of implementation and compensation for absences
Recommended optional programme components
Prerequisites and corequisites
Basic literature
Recommended reading