Course Details

Numerical methods 2

DAB035 course is part of 24 study plans

Ph.D. full-t. program DPC-M compulsory-elective Winter Semester 2nd year 10 credits

Ph.D. full-t. program DPC-K compulsory-elective Winter Semester 2nd year 10 credits

Ph.D. full-t. program DPC-V compulsory-elective Winter Semester 2nd year 10 credits

Ph.D. full-t. program DPC-E compulsory-elective Winter Semester 2nd year 10 credits

Ph.D. full-t. program DPC-S compulsory-elective Winter Semester 2nd year 10 credits

Ph.D. full-t. program DPC-GK compulsory-elective Winter Semester 2nd year 10 credits

Ph.D. combi. program DKC-S compulsory-elective Winter Semester 2nd year 10 credits

Ph.D. full-t. program DPA-S compulsory-elective Winter Semester 2nd year 10 credits

Ph.D. combi. program DKC-V compulsory-elective Winter Semester 2nd year 10 credits

Ph.D. full-t. program DPA-V compulsory-elective Winter Semester 2nd year 10 credits

Ph.D. combi. program DKC-M compulsory-elective Winter Semester 2nd year 10 credits

Ph.D. full-t. program DPA-M compulsory-elective Winter Semester 2nd year 10 credits

Ph.D. combi. program DKC-K compulsory-elective Winter Semester 2nd year 10 credits

Ph.D. full-t. program DPA-K compulsory-elective Winter Semester 2nd year 10 credits

Ph.D. combi. program DKC-E compulsory-elective Winter Semester 2nd year 10 credits

Ph.D. full-t. program DPA-E compulsory-elective Winter Semester 2nd year 10 credits

Ph.D. combi. program DKC-GK compulsory-elective Winter Semester 2nd year 10 credits

Ph.D. full-t. program DPA-GK compulsory-elective Winter Semester 2nd year 10 credits

Ph.D. combi. program DKA-GK compulsory-elective Winter Semester 2nd year 10 credits

Ph.D. combi. program DKA-S compulsory-elective Winter Semester 2nd year 10 credits

Ph.D. combi. program DKA-M compulsory-elective Winter Semester 2nd year 10 credits

Ph.D. combi. program DKA-K compulsory-elective Winter Semester 2nd year 10 credits

Ph.D. combi. program DKA-V compulsory-elective Winter Semester 2nd year 10 credits

Ph.D. combi. program DKA-E compulsory-elective Winter Semester 2nd year 10 credits

Mathematical approaches to the analysis of engineering problems, namely ordinary and partial differential equations, directed to numerical calculations - deeper knowledge than from the course DA01.

Course Guarantor

prof. Ing. Jiří Vala, CSc.

Institute

Institute of Mathematics and Descriptive Geometry

Learning outcomes

The aim of the course is to give students the overview of modern mathematical approaches to the analysis of engineering problems, to be able to apply them to concrete problems of their disciplines.It is intended as a continuation of the course DA61.

Prerequisites

At the level of the course DA61.

Corequisites

Not required.

Planned educational 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.

Forms and criteria of assessment

A student will only receive credit if he will solve individual problems assigned by the teacher. The final examination will be only a written one lasting 90 minutes and consisting of 4 problems to calculate.

Objective

Getting acquainted with the basics of the theory of numerical solution of ordinary differential equations and systems of such equations and second-order partial differential equations. Learning how to use numeric methods to solve such equations.

Specification of controlled instruction, the form of instruction, and the form of compensation of the absences

Vymezení kontrolované výuky a způsob jejího provádění stanoví každoročně aktualizovaná vyhláška garanta předmětu.

Lecture

3 hours/week, 13 weeks, elective

Syllabus of lectures

1. Formulation of the initial-value problem in ordinary differential equations of degree 1, basic properties, existence and uniqueness of solutions.
2. Basic numerical methods for the initial-value problems and their absolute stability.
3. Introduction to the variational calculus, basic spaces of integrable functions.
4. Classical and variational formulations of elliptic problems for ordinary differential equations of degree 2, basic physical meanings.
5. Standard finite difference method for elliptic problems for ordinary differential equations (ODE) of degree 2 and its stable modifications.
6. Approximation of boundary-value problems for second order ODE by the finite element method.
7. Classical and variational formulation of elliptic problems for fourth-order ODE and approximation by the finite element method.
8. Classical and variational formulation of elliptic problems for second-order partial differential equations.
9. Finite element method for elliptic problems in second-order partial differential equations.
10. Finite volume method.
11. Discretization of non-stationary problems for second-order differential equations by the method of straight-lines.
12. Mathematical models of flow. Nonlinear problems and problems with dominating convection.
13. Numerical methods for the models of flow.