SubjectsSubjects(version: 875)
Course, academic year 2020/2021
  
Methods of Numerical Mathematics I - NMAF013
Title: Metody numerické matematiky I
Guaranteed by: Department of Atmospheric Physics (32-KFA)
Faculty: Faculty of Mathematics and Physics
Actual: from 2020
Semester: winter
E-Credits: 3
Hours per week, examination: winter s.:2/0 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 II, 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 of numerical methods.

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, Wiley1998

A. Quarteroni, A. Valli: Numerical Approximation of Partial Differential Equations, Springer 1997

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

Lecture.

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

Examination - sylabus.

Syllabus -
Last update: BENESL/MFF.CUNI.CZ (05.05.2008)
Numerical solution of Linear systems
  • Direct methods - Gauss elimination. LU decomposition
  • Iterative methods - -Jacobi, Gauss-Seidel methods, relaxation methods, conjugate gradient method. GMRES
Nonlinear equations and systems of nonlinear equations.
Approximation and interpolation
  • Least square method
  • Lagrange and Newton interpolations, spline functions.
Numerical integration: Newton-Cotes formulas, Riachardson
  • extrapolation, Romberg integration.
Numerical solution of ODR - Cauchy problem
  • Basic concept - approximation, stability, convergence, truncation error, global error.
  • One-step methods - Runge-Kutta methods, method based on Taylor series

 
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