## M8PNM2 Advanced numerical methods II

Faculty of Science
Spring 2022
Extent and Intensity
2/2/0. 4 credit(s) (fasci plus compl plus > 4). Type of Completion: zk (examination).
Taught in person.
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
Prerequisites
M7PNM1 Advanced numerical methods I
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 course gives a survey of methods for numerical solving of differential equations (ordinary and partial).
(1) Students will acquire the most important methods for solving initial-value and boundary-value problems for ordinary differential equations and for solving the basic partial differential equations.
(2) 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.
(3) can apply some methods.
Learning outcomes
Student will be able to:
- design a suitable method for the numerical solution of the differential equation
- Implement the method using proprietary software
Syllabus
• 1. Introduction to nmerical solving of ODE: 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. Shooting method for solving boundary problems
• 5. Variational methods for ordinary and partial differential equations: Ritz method, Galerkin method.
• 6. Differences methods for ordinary and partial differential equations
Literature
• REKTORYS, Karel. Variační metody : v inženýrských problémech a v problémech matematické fyziky. Vyd. 6., opr. české 2. Praha: Academia, 1999. 602 s. ISBN 8020007148. info
• 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. Translated by Milan Práger - Emil Vitásek. 2. čes. vyd. Praha: Academia, 1978. 635 s., ob. info
Teaching methods
Lectures, class exercises
Assessment methods
Oral examination with preparation.
Language of instruction
Czech
Follow-Up Courses