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. Predictorcorrector 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.
