Course detail

Modern Numerical Methods

FEKT-LMNMAcad. year: 2012/2013

Numerical methods: Principle of numerical methods, classification and propagation of errores in a numerical process, encreasin of result accuracy, Banach fixed-point theorem.
Solving the systems of linear equations: review of finite and iterative methods of solution.
Solving the systems of nonlinear equations: review of one equation methods, Newton and iterative method for systems.
Solving the ordinary differential equations: initial value problems (one-step and multi-step methods, Taylor series method), boundary value problems (the finite difference, finite element anf finite volume methods).
Solving the partial differential equations: second-order equation classification, the finite difference, finite element and finite volume methods).

Language of instruction

Czech

Number of ECTS credits

Mode of study

Not applicable.

Guarantor

doc. RNDr. Jaromír Baštinec, CSc.

Department

Department of Mathematics (UMAT)

Learning outcomes of the course unit

The student is acquainted with some numerical methods for soluting the ordinary and partial differential equations.

Prerequisites

The subject knowledge on the Bachelor´s degree level is requested.

Co-requisites

Not applicable.

Planned learning activities and teaching methods

Teaching methods depend on the type of course unit as specified in the article 7 of BUT Rules for Studies and Examinations.

Assesment methods and criteria linked to learning outcomes

computer exercises max. 30 bodů, písemná semestrální zkouška max. 70 bodů

Course curriculum

Not applicable.

Work placements

Not applicable.

Aims

The aim is to extend and intesify knowledge from the previous courses, namely in connexion with practical applications of the methods for solving the ordinary a partial differential equations. For this purpose two chapters summarizing the methods for solving linear and nonlinear equations precede.

Specification of controlled education, way of implementation and compensation for absences

The content and forms of instruction in the evaluated course are specified by a regulation issued by the lecturer responsible for the course and updated for every academic year.

Recommended optional programme components

Not applicable.

Prerequisites and corequisites

Not applicable.

Basic literature

BAŠTINEC, J.; NOVÁK, M. Moderní numerické metody: sbírka příkladů. Brno: FEKT, VUT v Brně, 2011.

Type of course unit

Lecture

39 hod., optionally

Teacher / Lecturer

doc. RNDr. Michal Novák, Ph.D.

Syllabus

Examples of practical problems, principle of numeric methods, classification and propagation of errors.
Encreasing of result accuracy, Richardson extrapolation.
Complete metric space, contraction mapping, Banach fixed-point theorem and its use.
Finite, matrix-iterative and gradient-iterative methods for solution of linear equations.
Review of nethods for one nonlinear equation solution, Newton and iterative method for systems.
Ordinary differential equations, basic considerations and concepts.
Initial value problems, one-step methods, Runge-Kutta methods.
Taylor series method, principle of its algorithm, possibilities of its application.
Multi-step methods, methods based on numeric derivation and integration, predictor-corrector methods.
Boundary value problems, the finite difference, finite element and finite volume methods.
Partial differential equations, basic concepts, the second-order equation classification.
Finite difference method, finite element method.
Finite volume method, examples of numerical field computations.

Exercise in computer lab

13 hod., compulsory

Teacher / Lecturer

doc. RNDr. Michal Novák, Ph.D.

Syllabus

Computer laboratory fulfilling the lectures.

VUT

Faculties

University Institutes

Parts

Modern Numerical Methods

Type of course unit