Title:  Higly Sophisticated Computations 

Code:  VND 

Ac.Year:  2003/2004 

Sem:  Summer 

Language of Instruction:  Czech 

Completion:  examination (written) 

Type of instruction:  Hour/sem  Lectures  Seminar Exercises  Laboratory Exercises  Computer Exercises  Other 

Hours:  39  0  0  0  0 

 Exams  Tests  Exercises  Laboratories  Other 

Points:  0  0  0  0  0 



Guarantor:  Kunovský Jiří, doc. Ing., CSc. (DITS) 

Lecturer:  Kunovský Jiří, doc. Ing., CSc. (DITS) 
Faculty:  Faculty of Information Technology 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 implemented on oneprocessor systems (PC486, Pentium) and on multiprocessor systems. 
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. 
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 parallel FFT
 Simulation of electric circuits
 Solution of practical problems described by partial differential equations (investigating potentials, weather forecasting models)
 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, habilitační práce, VUT Brno, 1995

