Course detail

Numerical Methods II

FSI-SN2 Acad. year: 2026/2027 Summer semester

Supervisor

doc. Ing. Petr Tomášek, Ph.D.

Department

Institute of Mathematics

Learning outcomes of the course unit

Prerequisites

Differential and integral calculus for functions of one and more variables. Fundamentals of linear algebra. Ordinary differential equations. Numerical methods for solving linear and nonlinear equations. Interpolation. Basic programming skills.

Planned learning activities and teaching methods

Assesment methods and criteria linked to learning outcomes

Language of instruction

Czech

Aims

Specification of controlled education, way of implementation and compensation for absences

The study programmes with the given course

Programme B-MAI-P: Mathematical Engineering, Bachelor's
branch ---: no specialisation, 4 credits, compulsory

Programme B-MET-P: Mechatronics, Bachelor's
branch ---: no specialisation, 4 credits, compulsory

Programme C-AKR-P: , Lifelong learning
branch CLS: , 4 credits, elective

Type of course unit

 

Lecture

26 hours, optionally

Syllabus

1. Eigenvalue problems: basic knowledge.
2. Eigenvalue problems: power method, QR method.
3. Eigenvalue problems: Arnoldi method, Jacobi method, bisection method, computing the singular value decomposition.
4. Initial value problems for ODE1: basic notions (truncation error, stability,...)
5. Initial value problems for ODE1: Runge-Kutta methods, step control adjustment.
6. Initial value problems for ODE1: Adams methods, predictor-corrector technique.
7. Initial value problems for ODE1: backward differentiation formulas, stiff problems.
8. Boundary value problems for ODE2: shooting method, difference method, finite volume method.
9. Boundary value problems for ODE2: finite element method.
10. Elliptic PDEs: difference method, finite volume method.
11. Elliptic PDEs: finite element method.
12. Parabolic and hyperbolic PDEs: method of lines, stability, time discretization methods.
13. First order hyperbolic equation: method of lines, stability, method of characteristics.

Computer-assisted exercise

26 hours, compulsory

Syllabus

Students create elementary programs in MATLAB related to each subject-matter delivered at lectures and verify how the methods work. Furthermore students individually elaborate semester assignemets.