Course details

Advanced Computer Applications

APP Acad. year 2005/2006 Summer semester 6 credits

Current academic year

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 one-processor systems (PC486, Pentium) and on multi-processor systems.

Guarantor

Kunovský Jiří, doc. Ing., CSc.

Language of instruction

Czech

Completion

Examination

Time span

  • 39 hrs lectures
  • 26 hrs pc labs

Department

Department of Intelligent Systems (UITS)

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.

  • An individual solution of a nontrivial system of diferential equations.

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.

Prerequisite knowledge and skills

Numerical mathematics and theory of differential equations

Study literature

  • Hennessy, J.L., Patterson, D.A.: Computer Architecture: a Quantitative Approach, Morgan Kaufmann Publishers, Inc., 1990, San Mateo, California

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

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 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.

Syllabus of computer exercises

  1. Simulation system TKSL
  2. Exponential test example
  3. First order homogenous differential equation
  4. Second order homogenous differential equation
  5. Systems of linear algebraic equations
  6. Time function generation
  7. Arbitrary variable function generation
  8. Electronic circuits modeling
  9. Heat conduction equation
  10. Wave equation
  11. Laplace equation
  12. Control circuits
  13. Adjoint differential operators

Progress assessment

Study evaluation is based on marks obtained for specified items. Minimimum number of marks to pass is 50.

Controlled instruction

  • Mid-term written examination - 20 point
  • Final written examination - 80 points
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