SubjectsSubjects(version: 875)
Course, academic year 2020/2021
  
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 [hours/week]
Capacity: unlimited
Min. number of students: unlimited
State of the course: taught
Language: Czech, English
Teaching methods: full-time
Guarantor: doc. Ing. Luděk Beneš, Ph.D.
Mgr. Vladimír Fuka, Ph.D.
Classification: Physics > Mathematics for Physicists
Annotation -
Last update: BENESL/MFF.CUNI.CZ (05.05.2008)
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.
Aim of the course -
Last update: BENESL/MFF.CUNI.CZ (05.05.2008)

Fundamental methods for ODE and PDE.

Course completion requirements - Czech
Last update: 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

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

Lecture, laboratory exercise.

Requirements to the exam -
Last update: BENESL/MFF.CUNI.CZ (05.05.2008)

Examination - sylabus.

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

 
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