Nonlinear Differential Equations - NMNV535
Title: Nelineární diferenciální rovnice
Guaranteed by: Department of Numerical Mathematics (32-KNM)
Faculty: Faculty of Mathematics and Physics
Actual: from 2020
Semester: winter
E-Credits: 3
Hours per week, examination: winter 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, English
Teaching methods: full-time
Teaching methods: full-time
Guarantor: RNDr. Miloslav Vlasák, Ph.D.
Class: M Mgr. NVM
M Mgr. NVM > Povinně volitelné
Classification: Mathematics > Differential Equations, Potential Theory, Numerical Analysis
Incompatibility : NDIR050
Interchangeability : NDIR050
Is interchangeable with: NDIR050
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Annotation -
Last update: T_KNM (02.04.2015)
Nonlinear differential equations in divergence form. Carathéodory grow condition, Nemycki operator. Variational methods and applications of theory of monotone a potential operators. Numerical solution of nonlinear differential equations by abstract numerical methods. Existence of the solution, stability, consistency and convergence of abstract numerical methods.
Course completion requirements -
Last update: prof. RNDr. Vít Dolejší, Ph.D., DSc. (07.06.2019)

Oral examination according to sylabus.
Literature -
Last update: T_KNM (15.09.2013)

DOLEJŠÍ V., NAJZAR K. Nelineární funkcionální analýza, 2011, skripta MFF UK, 202 s. ISBN 978-80-7378-137-8

FUČÍK S., KUFNER A. Nelineární diferenciální rovnice, 1978, SNTL, 344 s.

ZEIDLER E. Nonlinear functional analysis and its applications I, II, III, 1984, 1985, 1986, Springer

BÖHMER K. Numerical methods for nonlinear elliptic differential equations 2010, Oxford University Press. xxvii, 746s.

ISBN 978-0-19-957704-0
Requirements to the exam -
Last update: RNDr. Miloslav Vlasák, Ph.D. (11.10.2017)

Oral examination of topics discussed at the lectures.
Syllabus -
Last update: T_KNM (15.09.2013)

Nonlinear differential equations in divergence form.

Caratheodory growth condition, Nemycky operators.

Variational methods and aplication of theory of monotone and potential operator, proof of existence of solution.

Numerical solution of nonlinear diferential equation by abstract numerical method.

Existence of solution, stability, consistency, convergence of abstract numerical method.

Application on conforming finite element method and discontinuous Galerkin method.
Entry requirements -
Last update: RNDr. Miloslav Vlasák, Ph.D. (12.05.2018)

Basic knowledge of mathematical analysis, finite element method, ordinary differential equations and partial differential equations. Knowledge of nonlinear functional analysis.