Numerical Methods II (FSI-SN2)

Academic year 2026/2027
Supervisor: doc. Ing. Petr Tomášek, Ph.D.  
Supervising institute: ÚM all courses guaranted by this institute
Teaching language: Czech
Course type: departmental course
Aims of the course unit:
 
Learning outcomes and competences:
 
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.
Course contents:
 
Teaching methods and criteria:
 
Assesment methods and criteria linked to learning outcomes:
 
Controlled participation in lessons:
 
Type of course unit:
    Lecture  13 × 2 hrs. optionally                  
    Computer-assisted exercise  13 × 2 hrs. compulsory                  
Course curriculum:
    Lecture 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 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.
Literature - fundamental:
1. M.T. Heath: Scientific Computing. An Introductory Survey. Second edition. McGraw-Hill, New York, 2002.
2. L.F. Shampine: Numerical Solution of Ordinary Differential Equations, Chapman & Hall, New York, 1994.
3. E. Vitásek: Základy teorie numerických metod pro řešení diferenciálních rovnic. Academia, Praha, 1994.
5. C. F. Van Loan, G. H. Golub: Matrix Computations, 3th ed., the Johns Hopkins University Press, Baltimore, 1996.
Literature - recommended:
1. L. Čermák: Numerické metody pro řešení diferenciálních rovnic, [online], available from: http://mathonline.fme.vutbr.cz/Numericke-metody-II/sc-1246-sr-1-a-263/default.aspx.
2. L. Čermák: Vybrané statě z numerických metod. [on-line], available from: http://mathonline.fme.vutbr.cz/Numericke-metody-II/sc-1227-sr-1-a-238/default.aspx.
The study programmes with the given course:
Programme Study form Branch Spec. Final classification   Course-unit credits     Obligation     Level     Year     Semester  
B-MAI-P full-time study --- no specialisation -- Cr,Ex 4 Compulsory 1 3 S
B-MET-P full-time study --- no specialisation -- Cr,Ex 4 Compulsory 1 3 S
C-AKR-P full-time study CLS -- Cr,Ex 4 Elective 1 1 S