Course: Numerical Solution of Differencial Equations 1

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Course title Numerical Solution of Differencial Equations 1
Course code KMA/NDR1
Organizational form of instruction Lecture + Exercise
Level of course Master
Year of study not specified
Semester Winter
Number of ECTS credits 3
Language of instruction Czech
Status of course Compulsory-optional, Optional
Form of instruction Face-to-face
Work placements This is not an internship
Recommended optional programme components None
Lecturer(s)
  • Ženčák Pavel, RNDr. Ph.D.
Course content
1. Initial value problems for ODE, existence and uniqueness of solution. 2. Solution using Taylor series method. 3. Implementation of iteration methods. 4. Singlestep methods - basic concepts and the way of development. Survey of the most used singlestep methods. Convergence and stability. Implementation in Matlab. 5. Linear multistep methods - basic concepts of development. Basic classification of linear multistep methods (explicit, implicit) and their properties. Consistency, order, stability and convergence of linear multistep methods. 6. Predictor-corrector implementation of linear multistep methods, error control, control of integration step and integration step size adjustment, extrapolation methods. 7. Stiff problems. 8. General linear methods. 9. Boundary value problems for ODE and their basic properties. Method of collocations, shooting method. 10. Finite difference method - principles, implementation and convergence.

Learning activities and teaching methods
Monologic Lecture(Interpretation, Training), Demonstration
  • Attendace - 39 hours per semester
  • Semestral Work - 50 hours per semester
Learning outcomes
The course introduces numerical methods for solving ordinary differential equations.
Comprehension Understand the numerical methods for solution of ordinary differential equations.
Prerequisites
Basic knowledge of numerical methods, theory of differential equations and programming in Matlabu.

Assessment methods and criteria
Oral exam, Seminar Work

Credit: course work (including program development).
Recommended literature
  • E. Vitásek. (1994). Základy teorie numerických metod pro řešení diferenciálních rovnic. Academia, Praha.
  • Hairer, E., & Wanner, G. (1996). Solving ordinary differential equations. Berlin: Springer.
  • Hairer, E., Norsett, S. P., & Wanner, G. (1993). Solving ordinary differential equations. Berlin: Springer.
  • S. Míka, P. Přikryl. (1994). Numerické metody řešení ODR. Skripta ZČU, Plzeň.


Study plans that include the course
Faculty Study plan (Version) Branch of study Category Recommended year of study Recommended semester
Faculty of Science General Physics and Mathematical Physics (2014) Physics courses 1 Winter
Faculty of Science Applied Mathematics (2014) Mathematics courses 1 Winter
Faculty of Science Applications of Mathematics in Economy (2015) Mathematics courses - Winter