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Methods of Numerical Mathematics II - NMAF014

Title:	Metody numerické matematiky II
Guaranteed by:	Department of Atmospheric Physics (32-KFA)
Faculty:	Faculty of Mathematics and Physics
Actual:	from 2020
Semester:	summer
E-Credits:	6
Hours per week, examination:	summer s.:2/2, C+Ex [HT]
Capacity:	unlimited
Min. number of students:	unlimited
4EU+:	no
Virtual mobility / capacity:	no
State of the course:	taught
Language:	Czech, English
Teaching methods:	full-time

Guarantor:	doc. Ing. Luděk Beneš, Ph.D. Mgr. Vladimír Fuka, Ph.D.
Teacher(s):	doc. Ing. Luděk Beneš, Ph.D.
Classification:	Physics > Mathematics for Physicists

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Annotation -

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: BENESL/MFF.CUNI.CZ (05.05.2008)

Aim of the course -

Fundamental methods for ODE and PDE.

Last update: BENESL/MFF.CUNI.CZ (05.05.2008)

Course completion requirements - Czech

Zkouška - viz sylabus.

Last update: Mikšovský Jiří, doc. Mgr., Ph.D. (13.02.2019)

Literature -

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: BENESL/MFF.CUNI.CZ (05.05.2008)

Teaching methods -

Lecture, laboratory exercise.

Last update: BENESL/MFF.CUNI.CZ (05.05.2008)

Requirements to the exam -

Examination - sylabus.

Last update: BENESL/MFF.CUNI.CZ (05.05.2008)

Syllabus -

Numerical solution of ODR - Cauchy problem

Linear multi-step methods - Adams-Bashforth method. Adams-Moulton method, predictor-corector, stability, stiff equations.

Numerical solution of ODR - boundary value problem

Shooting method

Finite difference approximation,stability, consistency, convergence.

Variation formulation, Galerkin method.

Partial differential equations

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

Advection equation - finite differences, methods of lines. Lax-Friedrichs. Lax-Wendroff. upwind methods. Beam-Warming. stability.

Hyperbolic systems

Last update: Beneš Luděk, doc. Ing., Ph.D. (29.04.2020)