Title:  Highly Sophisticated Computations 

Code:  VND 

Ac.Year:  2017/2018 

Term:  Summer 

Curriculums:  

Language of Instruction:  Czech 

Completion:  examination (written) 

Type of instruction:  Hour/sem  Lectures  Sem. Exercises  Lab. exercises  Comp. exercises  Other 

Hours:  39  0  0  26  0 

 Examination  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 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.  Generic learning outcomes and competences: 

 
 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 highorder 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. SpringerVerlag Berlin Heidelberg,
1987, ISBN 3540171452
 Hairer,E., Norsett,S.P.,Wanner,G.: Solving Ordinary Differential
Equations II, second revised ed., vol. Stiff and DifferentialAlgebraic Problems. SpringerVerlag Berlin Heidelberg,
1996, ISBN 3540604522
 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.  
