The course, together with the Methods of Numerical Mathematics I, covers
fundamentals of the numerical mathematics. The course is devoted to
mathematical modelling and numerical solution of the ordinary and partial
differential equations.
Last update: doc. Mgr. Jiří Mikšovský, Ph.D. (13.02.2019)
Aplikace numerických metod v meteorologii.
Aim of the course -
Last update: BENESL/MFF.CUNI.CZ (05.05.2008)
Fundamental methods for ODE and PDE.
Last update: BENESL/MFF.CUNI.CZ (05.05.2008)
Základní metody pro ODR a PDR.
Course completion requirements - Czech
Last update: doc. Mgr. Jiří Mikšovský, Ph.D. (13.02.2019)
Zkouška - viz sylabus.
Literature -
Last update: BENESL/MFF.CUNI.CZ (05.05.2008)
A. Ralston: Základy numerické matematiky, Academia Praha 1973
E. Vitásek: Numerické metody, SNTL Praha 1987
R. J. LeVaque: Finite Difference Methods for Differential Equations
J.H. Ferzinger: Numerical Methods for Engineering Applications, Wiley 1998
A. Quarteroni, A. Valli: Numerical Approximation of Partial Differential Equations, Springer 1997
Last update: doc. Mgr. Jiří Mikšovský, Ph.D. (13.02.2019)
A. Ralston: Základy numerické matematiky, Academia Praha 1973
E. Vitásek: Numerické metody, SNTL Praha 1987
R. J. LeVeque: Finite Difference Methods for Differential Equations
J.H. Ferziger: Numerical Methods for Engineering Applications, Wiley 1998
A. Quarteroni, A. Valli: Numerical Approximation of Partial Differential Equations, Springer 1997
P. Mote and A. O'Neill: Numerical Modeling of the Global Atmosphere in the Climate System, NATO Science Series, Kluwer 2000
Teaching methods -
Last update: BENESL/MFF.CUNI.CZ (05.05.2008)
Lecture, laboratory exercise.
Last update: doc. Mgr. Jiří Mikšovský, Ph.D. (13.02.2019)
Přednáška, cvičení - samostatné programování modelových příkladů.
Requirements to the exam -
Last update: BENESL/MFF.CUNI.CZ (05.05.2008)
Examination - sylabus.
Last update: BENESL/MFF.CUNI.CZ (05.05.2008)
Zkouška - viz. sylabus.
Syllabus -
Last update: doc. Ing. Luděk Beneš, Ph.D. (29.04.2020)
Classification, Fourier analysis of linear PDE, characteristics, convergence, consistence, stability, FD methods, methods of lines, CFL condition, von Neumann analysis.
Elliptic equations - discretisation, finite differences, five and nine-point scheme, boundary conditions, solving the linear system, accuracy and stability.
Diffusion equation- finite differences, method of lines. Crank-Nicolson method. LOD and ADI method