M9100 Numerical methods for solving ordinary differential equations

Faculty of Science
Autumn 2016
Extent and Intensity
2/1/0. 3 credit(s) (příf plus uk k 1 zk 2 plus 1 > 4). Type of Completion: zk (examination).
Teacher(s)
Mgr. Jiří Zelinka, Dr. (lecturer)
Guaranteed by
doc. PaedDr. RNDr. Stanislav Katina, Ph.D.
Department of Mathematics and Statistics – Departments – Faculty of Science
Supplier department: Department of Mathematics and Statistics – Departments – Faculty of Science
Timetable
Mon 19. 9. to Sun 18. 12. Mon 8:00–9:50 M6,01011
  • Timetable of Seminar Groups:
M9100/01: Mon 19. 9. to Sun 18. 12. Mon 15:00–15:50 M6,01011, J. Zelinka
Prerequisites
Basic numerical methods of mathematical analysis and linear algebra. Basis of functional analysis
Course Enrolment Limitations
The course is also offered to the students of the fields other than those the course is directly associated with.
fields of study / plans the course is directly associated with
Abstract
The course gives a survey of methods for numerical solving of differential equations (ordinary and partial).
Students will acquire the most important methods for solving initial-value, boundary-value problems for ordinary differential equations.
At the end of this course, students will be able to compare the methods not only from the theoretical point of view, but they will understand them from the point of stability, efficiency, etc.
Key topics
  • 1. Introduction: The solvability of differential equations, approximate solutions, error, stability.
  • 2. One-step methods: Euler method, Taylor series method, Runge-Kutta methods
  • 3. Multistep methods: Adams methods, predictor-corrector
  • 4. Boundary value problems: shooting method, method of differences
  • 5. Variational methods: Ritz method, Galerkin method.
Study resources and literature
  • VITÁSEK, Emil. Základy teorie numerických metod pro řešení diferenciálních rovnic. 1. vyd. Praha: Academia, 1994, 409 s. ISBN 8020002812. info
  • BABUŠKA, Ivo and Milan PRÁGER. Numerické řešení diferanciálních rovnic (Numerical solution of differential equations). 1st ed. Praha: Státní nakladatelství technické literatury, 1964, 238 pp. info
  • RALSTON, Anthony. Základy numerické matematiky. 1. české vyd. Praha: Academia, 1973, 635 s. URL info
Approaches, practices, and methods used in teaching
Lectures, class exercises
Method of verifying learning outcomes and course completion requirements
Oral examination with preparation.
Language of instruction
Czech
Follow-Up Courses
Further comments (probably available only in Czech)
Study Materials
The course is taught annually.
General note: Pro zapsání předmětu je třeba zná tzákladní numerické metody matematické analýzy a lineární algebry a základy funkcionální analýzy.
The course is also listed under the following terms Autumn 2007 - for the purpose of the accreditation, Autumn 1999, Autumn 2010 - only for the accreditation, Autumn 2000, Autumn 2001, Autumn 2002, Autumn 2003, Autumn 2004, Autumn 2005, Autumn 2006, Autumn 2007, Autumn 2008, Autumn 2009, Autumn 2010, Autumn 2011, Autumn 2011 - acreditation, Autumn 2012, Autumn 2013, Autumn 2014, Autumn 2015, autumn 2017, Autumn 2018, Autumn 2019.
  • Enrolment Statistics (Autumn 2016, recent)
  • Permalink: https://is.muni.cz/course/sci/autumn2016/M9100