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Numerical Solution of Nonstationary Problems - NNUM111

Title:	Numerické řešení nestacionárních úloh
Guaranteed by:	Department of Numerical Mathematics (32-KNM)
Faculty:	Faculty of Mathematics and Physics
Actual:	from 2014 to 2017
Semester:	summer
E-Credits:	6
Hours per week, examination:	summer s.:2/0, Ex [HT]
Capacity:	unlimited
Min. number of students:	unlimited
4EU+:	no
Virtual mobility / capacity:	no
State of the course:	not taught
Language:	Czech
Teaching methods:	full-time
Teaching methods:	full-time

Guarantor:	doc. RNDr. Václav Kučera, Ph.D.
Class:	DS, vědecko - technické výpočty
Classification:	Mathematics > Numerical Analysis

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Annotation -

Last update: T_KNM (15.01.2007)

The fundamental theoretical and practical aspects of a solution of evolutional problems. Survey of most used numerical methods.

Aim of the course -

Last update: T_KNM (17.05.2008)

Knowledge about variational methods and numerical solution of nonstationary problems.

Literature - Czech

Last update: T_KNM (17.05.2008)

Rektorys K.: Metoda časové diskretizace a parciální diferenciální rovnice, SNTL, l985

Teaching methods -

Last update: T_KNM (17.05.2008)

Lectures in a lecture hall.

Requirements to the exam -

Last update: T_KNM (17.05.2008)

Examination according to the syllabus.

Syllabus -

Last update: T_KNM (26.03.2009)

The method of time-discretization, Rothe`s function.

Variational methods, the theorem on minimum of energy functional, generalized solution, theorem on existence and uniqueness of the solution, Ritz`s method, Galerkin method, FEM.

Lax-Milgram theorem, week solution, stable and instable boundary conditions.

Theoretical aspects of time discretization. The existence theorem for the special linear parabolic problem, abstract functions, the Bochner integral, regularity properties of a week solution, nonhomogeneous initial and boundary conditions, very week solution and its regularity. Convergence of Ritz`s-Rothe`s method.

Hyperbolic problems, homogeneous and nonhomogeneous initial conditions.

Nonhomogeneous instable boundary conditions.

Problems: Elliptic problems, parabolic problems, hyperbolic problems, special problems.

Entry requirements -

Last update: T_KNM (17.05.2008)

There are no special entry requirements.