Course Details

Numerical methods II

DA63 course is part of 22 study plans

Ph.D. full-t. program nD > PST compulsory-elective Winter Semester 2nd year 10 credits

Ph.D. full-t. program nD > FMI compulsory-elective Winter Semester 2nd year 10 credits

Ph.D. full-t. program nD > KDS compulsory-elective Winter Semester 2nd year 10 credits

Ph.D. full-t. program nD > MGS compulsory-elective Winter Semester 2nd year 10 credits

Ph.D. full-t. program nD > VHS compulsory-elective Winter Semester 2nd year 10 credits

Ph.D. combi. program nDK > PST compulsory-elective Winter Semester 2nd year 10 credits

Ph.D. combi. program nDK > KDS compulsory-elective Winter Semester 2nd year 10 credits

Ph.D. combi. program nDK > VHS compulsory-elective Winter Semester 2nd year 10 credits

Ph.D. combi. program nDK > FMI compulsory-elective Winter Semester 2nd year 10 credits

Ph.D. combi. program nDK > MGS compulsory-elective Winter Semester 2nd year 10 credits

Ph.D. full-t. program nDA > PST compulsory-elective Winter Semester 2nd year 10 credits

Ph.D. full-t. program nDA > FMI compulsory-elective Winter Semester 2nd year 10 credits

Ph.D. full-t. program nDA > KDS compulsory-elective Winter Semester 2nd year 10 credits

Ph.D. full-t. program nDA > MGS compulsory-elective Winter Semester 2nd year 10 credits

Ph.D. full-t. program nDA > VHS compulsory-elective Winter Semester 2nd year 10 credits

Ph.D. combi. program nDKA > PST compulsory-elective Winter Semester 2nd year 10 credits

Ph.D. combi. program nDKA > FMI compulsory-elective Winter Semester 2nd year 10 credits

Ph.D. combi. program nDKA > KDS compulsory-elective Winter Semester 2nd year 10 credits

Ph.D. combi. program nDKA > MGS compulsory-elective Winter Semester 2nd year 10 credits

Ph.D. combi. program nDKA > VHS compulsory-elective Winter Semester 2nd year 10 credits

Ph.D. full-t. program I > GAK compulsory-elective Winter Semester 2nd year 10 credits

Ph.D. combi. program IK > GAK compulsory-elective Winter Semester 2nd year 10 credits

Numerical methods for the initial-value problem for one ordinary differential equation (ODE) of order one and for systems of ODE of order one, absolute stability, variational formulation of boundary-value problems for ODE and partial DE of order two, discretization of elliptic differential problems by the finite difference and the finite element methods, numerical methods for the non-stationary parabolic and hyperbolic differential problems, numerical solution of a nonlinear differential boundary-value problem.

Course Guarantor

prof. Ing. Jiří Vala, CSc.

Institute

Institute of Mathematics and Descriptive Geometry

Prerequisites

Differential and integral calculus of one- and two-functions, interpolation and approximation of functions, numeric differentiation and intgration, numerical linear algebra.

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.

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.