M9100 Numerical methods for solving differential equations

Faculty of Science
Autumn 2007 - for the purpose of the accreditation
Extent and Intensity
2/1/0. 3 credit(s) (fasci plus compl plus > 4). Type of Completion: zk (examination).
Teacher(s)
doc. RNDr. Ladislav Adamec, CSc. (lecturer)
Guaranteed by
prof. RNDr. Ivanka Horová, CSc.
Department of Mathematics and Statistics - Departments - Faculty of Science
Contact Person: prof. RNDr. Ivanka Horová, CSc.
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
Course objectives
The solving of large technical and scientific problems can be often modeled by means of differential equations.Practical solving of such problems consists in application of suitable numerical method. This course aims to give a survey of methods for numerical solving of differential equations.The most important methods for solving of initial-value and boundary-value problems for ordinary equations and methods for partial differential equations are introduced. Particular methods are not only described from the theoretical point of view,but they are also reviewed from the point of view of stability,efficiency ,etc.The practical examples indicate the possible characteristic difficulties in applications.
Syllabus
  • Variational methods for solving ordinary and partial differential equations:Ritz method,Galerkin method. Methods for solving ordinary differential equations : 1.Initial-value problems (Runge -Kutta methods,multistep methods). 2.Boundary-value problems (shooting method,difference methods) Methods for solving partial differential equations: Finite -difference method,convergence and stability of difference schemes.
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). 1. vyd. Praha: Státní nakladatelství technické literatury, 1964. 238 pp. info
  • REKTORYS, Karel. Metoda časové diskretizace a parciální diferenciální rovnice. 2. vyd. Praha: SNTL - Nakladatelství technické literatury, 1985. 361 s. info
  • RALSTON, Anthony. Základy numerické matematiky. Translated by Milan Práger - Emil Vitásek. 2. čes. vyd. Praha: Academia, 1978. 635 s., ob. info
Assessment methods (in Czech)
Přednáška,cvičení částečně v počítačové učebně. Zkouška :ústní.
Language of instruction
Czech
Follow-Up Courses
Further comments (probably available only in Czech)
The course can also be completed outside the examination period.
The course is taught annually.
The course is taught: every week.
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 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 2016, autumn 2017, Autumn 2018, Autumn 2019.