Title: | Highly Sophisticated Computations |
---|
Code: | VND |
---|
Ac.Year: | 2017/2018 |
---|
Sem: | Summer |
---|
Curriculums: | |
---|
Language of Instruction: | Czech |
---|
Completion: | examination (written) |
---|
Type of instruction: | Hour/sem | Lectures | Seminar Exercises | Laboratory Exercises | Computer Exercises | Other |
---|
Hours: | 39 | 0 | 0 | 26 | 0 |
---|
| Exams | Tests | Exercises | Laboratories | Other |
---|
Points: | 60 | 20 | 0 | 20 | 0 |
---|
|
---|
Guarantor: | Kunovský Jiří, doc. Ing., CSc. (DITS) |
---|
Lecturer: | Kunovský Jiří, doc. Ing., CSc. (DITS) |
Instructor: | Šátek Václav, Ing., Ph.D. (DITS) |
---|
Faculty: | Faculty of Information Technology BUT |
---|
Department: | Department of Intelligent Systems FIT BUT |
---|
| 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. | Description: |
---|
| | 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.
Topics for Final exam:
- Analytic solution of differential equations.
- Numeric solution of differential equations.
- Extremely accurate solution of differential equations using Taylor series method.
- Parallel properties of Taylor series method, basic programming of specialised parallel problems by methods using the calculus (close relationship of equation and block representation of the problem).
- 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 (ODEs).
- Fourier series and finite integrals - solution using ODEs.
- Simulation of electric circuit.
- Solution of practical problems described by partial differential equation.
- Conception of the elementary processor of a specialised parallel computation system.
| Knowledge and skills required for the course: |
---|
| | Numerical Mathematics
| Subject specific learning outcomes and competencies: |
---|
| | 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. | Generic learning outcomes and competencies: |
---|
| |
- An individual solution of a nontrivial system of diferential equations.
| 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.
| Fundamental literature: |
---|
|
- Hennessy, J. L., Patterson, D.A.: Computer Architecture: a
Quantitative Approach, Morgan Kaufmann Publishers, Inc., 1990, San
Mateo, California
- Kunovský, J.: Modern Taylor Series Method, habilitation work, VUT Brno, 1995
- Hairer,E., Norsett,S.P.,Wanner,G.: Solving Ordinary Differential
Equations I, vol. Nonstiff Problems. Springer-Verlag Berlin Heidelberg,
1987, ISBN 3-54017145-2
- Hairer,E., Norsett,S.P.,Wanner,G.: Solving Ordinary Differential
Equations II, second revised ed., vol. Stiff and Differential-Algebraic Problems. Springer-Verlag Berlin Heidelberg,
1996, ISBN 3-540-60452-2
| Controlled instruction: |
---|
| | Submission of report on the results of experiments carried out within the tutorial. Any laboratory should be replaced in the final weeks of the semester. | Progress assessment: |
---|
| | Half Term Exam and Term Exam. The minimal number of points which can
be obtained from the final exam is 29. Otherwise, no points will
be assigned to a student. | |
|