714-0927/01 – The numerical solution of ordinary differential equations (NŘODR)

Gurantor departmentDepartment of Mathematics and Descriptive GeometryCredits0
Subject guarantorRNDr. Břetislav Krček, CSc.Subject version guarantorRNDr. Břetislav Krček, CSc.
Study levelpostgraduateRequirementChoice-compulsory
YearSemesterwinter + summer
Study languageCzech
Year of introduction1996/1997Year of cancellation2008/2009
Intended for the facultiesIntended for study typesDoctoral
Instruction secured by
LoginNameTuitorTeacher giving lectures
KRC20 RNDr. Břetislav Krček, CSc.
Extent of instruction for forms of study
Form of studyWay of compl.Extent
Full-time Credit and Examination 0+0
Combined Credit and Examination 0+0

Subject aims expressed by acquired skills and competences

The principles of the ordinary differential equations numerical solution. The basic one-step and multi-step methods.

Teaching methods

Individual consultations
Other activities

Summary

The intention of the first part of the subject is to make deeper students’ general knowledge about the ordinary differential equations and their systems. In the second (main) part of the subject the numerical solution of the initial problems for the ordinary differential equations and their systems is taught.

Compulsory literature:

Lambert, J.D.: Computational Methods in Ordinary Differential Equations. London – New York – Sydney – Toronto: J. Wiley and Sons 1973.

Recommended literature:

Henrici, P.: Discrete Variable Methods in Ordinary Differential Equations. New York – London : J. Wiley and Sons 1962. Lapidus, L. – Seinfeld, J.H.: Numerical Solution of Ordinary Differential Equations. New York – London : Academic Press 1971.

Way of continuous check of knowledge in the course of semester

E-learning

Další požadavky na studenta

Prerequisities

Subject has no prerequisities.

Co-requisities

Subject has no co-requisities.

Subject syllabus:

Úvod Terminologie, třídění diferenciálních rovnic (DR) a jejich soustav Počáteční úlohy Převod DR rovnic vyššího řádu na soustavy DR prvního řádu Existence a jednoznačnost řešení počáteční úlohy Lipschitzova podmínka, podmínka vyjádřená pomocí parciálních derivací Podmíněnost počátečních úloh Numerické metody pro řešení počátečních úloh Princip metod pro řešení počátečních úloh Eulerova metoda Řád metody Chyby aproximace Konvergence metody Řád metody, řád Eulerovy metody a globální chyba Eulerovy metody Vliv zaokrouhlovacích chyb a odhad chyby metodou polovičního kroku Jednokrokové metody Metody Taylorova typu Metody Rungova-Kuttova typu, odhad chyby Vícekrokové metody Lineární k-kroková metoda Diskretizační chyba Přehled některých vícekrokových metod Stabilita řešení, výběr metody pro řešení počáteční úlohy

Conditions for subject completion

Full-time form (validity from: 1960/1961 Summer semester, validity until: 2012/2013 Summer semester)
Task nameType of taskMax. number of points
(act. for subtasks)
Min. number of points
Exercises evaluation and Examination Credit and Examination 100 (100) 51
        Examination Examination 100  0
        Exercises evaluation Credit  
Mandatory attendence parzicipation:

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Occurrence in study plans

Academic yearProgrammeField of studySpec.FormStudy language Tut. centreYearWSType of duty
2007/2008 (P2645) Electrical Engineering, Communication and Computer systems (2612V045) Technical Cybernetics P Czech Ostrava Choice-compulsory study plan
2006/2007 (P2645) Electrical Engineering, Communication and Computer systems (2612V045) Technical Cybernetics P Czech Ostrava Choice-compulsory study plan
2005/2006 (P2645) Electrical Engineering, Communication and Computer systems (2612V045) Technical Cybernetics P Czech Ostrava Choice-compulsory study plan
2004/2005 (P2301) Mechanical Engineering (2302V002) Parts of Machines and Mechanisms P Czech Ostrava 1 Choice-compulsory study plan
2004/2005 (P2645) Electrical Engineering, Communication and Computer systems (2612V045) Technical Cybernetics P Czech Ostrava Choice-compulsory study plan
2003/2004 (P2645) Electrical Engineering, Communication and Computer systems (2612V045) Technical Cybernetics P Czech Ostrava Choice-compulsory study plan
2001/2002 (P2301) Mechanical Engineering (2302V002) Parts of Machines and Mechanisms P Czech Ostrava 1 Choice-compulsory study plan
2001/2002 (P2301) Mechanical Engineering (2302V006) Energy Engineering P Czech Ostrava 1 Choice-compulsory study plan
2001/2002 (P2301) Mechanical Engineering (2303V002) Mechanical Engineering Technology P Czech Ostrava 1 Choice-compulsory study plan
2001/2002 (P2301) Mechanical Engineering (3901V003) Applied Mechanics P Czech Ostrava 1 Choice-compulsory study plan
2001/2002 (P2301) Mechanical Engineering (2302V002) Parts of Machines and Mechanisms P Czech Ostrava 1 Choice-compulsory study plan

Occurrence in special blocks

Block nameAcademic yearForm of studyStudy language YearWSType of blockBlock owner