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Numerical Solution of Partial Differential Equations - NMNM338

Title:	Numerické řešení parciálních diferenciálních rovnic
Guaranteed by:	Department of Numerical Mathematics (32-KNM)
Faculty:	Faculty of Mathematics and Physics
Actual:	from 2021
Semester:	summer
E-Credits:	5
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
Teaching methods:	full-time
Teaching methods:	full-time

Guarantor:	doc. Mgr. Petr Knobloch, Dr., DSc.
Class:	M Bc. OM M Bc. OM > Zaměření MA M Bc. OM > Zaměření NUMMOD M Bc. OM > Povinně volitelné
Classification:	Mathematics > Differential Equations, Potential Theory
Incompatibility :	NMMA334
Interchangeability :	NMMA334
Is pre-requisite for:	NMNM351
In complex interchangeability with:	NMMA334
In complex incompatibility with:	NMMA334

Opinion survey results Examination dates SS schedule Noticeboard

Annotation -

Last update: doc. RNDr. Petr Tichý, Ph.D. (25.07.2021)

An introductory course in numerical solution of partial differential equations for bachelor's program in General Mathematics. Recommended for specializations Mathematical Analysis and Mathematical Modelling and Numerical Analysis.

Course completion requirements -

Last update: doc. Mgr. Petr Kaplický, Ph.D. (29.05.2019)

Credit for the exercise is granted for activity at the exercise throughout the semester.

Literature - Czech

Last update: doc. Mgr. Petr Knobloch, Dr., DSc. (22.07.2021)

K. W. Morton, D. F. Mayers: Numerical solution of partial differential equations, 2nd ed., Cambridge University Press, Cambridge, 2005

J. C. Strikwerda: Finite difference schemes and partial differential equations, 2nd ed., SIAM, Philadelphia, 2004

R. J. LeVeque: Finite difference methods for ordinary and partial differential equations: steady-state and time-dependent problems, SIAM, Philadelphia, 2007

J. W. Thomas: Numerical partial differential equations: finite difference methods, Springer, New York, 1995

A. Quarteroni, A. Valli: Numerical approximation of partial differential equations, 2nd ed., Springer, 2008

M. Feistauer: Diskrétní metody řešení diferenciálních rovnic, skripta, SPN, Praha, 1981.

Requirements to the exam -

Last update: doc. Mgr. Petr Knobloch, Dr., DSc. (22.07.2021)

The exam consists of a written part and an oral part. In the written part the calculation techniques will be tested at the extent considered during the tutorials. After succeeding in the written part the students will continue with the oral part. The theory including the proofs at the extent considered during the lectures will be examined.

Syllabus -

Last update: doc. Mgr. Petr Knobloch, Dr., DSc. (22.07.2021)

Introduction to the finite difference method.

Numerical solution of the transport equation.

Numerical solution of the mixed problem for the heat equation in 1D.

Analysis of a general scheme for equations of 1st order in time.

Numerical solution of elliptic equations.

Entry requirements -

Last update: doc. Mgr. Petr Kaplický, Ph.D. (29.05.2019)

Knowledge of mathematical analysis on the level of obligatory courses recommended for the first two years of the study branch General Mathematics is expected.